Potions:
Potion of Healing (Common) 3d4+3 (modified from the book's 2d4 + 2)
Potion of Greater Healing (Uncommon) 6d4+6 (modified from the book's 4d4 + 4)
Potion of Superior Healing (Rare) 12d4+12 (modified from the book's 8d4 + 8)
Potion of Supreme Healing (Very rare) 15d4+20 (modified from the book's 10d4 + 20)
Ki Confluence Potion (Very rare) You can draw ki equal to your proficiency bonus back into your body. For each ki drawn back in this way, gain 10 hit points.
Restore Potion (Legendary) - Heals all injuries and any manner of ailment, including recent death, completely.

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Suitable for this thread:
Custom items that aren't precious conjuncts.
Modified stock items.
Not listed in this thread:
Standard magical items (these exist online)
Precious Conjuncts (these have their own PDF)
Items with their own threads, like the Branch of Palendis ( viewtopic.php?f=23&t=538 )
Term glossary:
Items that use terms like "bind" or "unbind" represent a state defined in the item and pertinent only there.
Items that use the highlighted term "attunement" use all the attunement rules normal for 5e, which includes a limit of three attuned items at the same time. Note that high level artificers can attune more than three items at a time.
Items that use the highlight term "soulbound", borrowed from video games, are items that are more or less a part of you in some fashion, and have a mechanic to recreate the item if it is destroyed or lost. Willingly selling the item removes this feature, as does being dead for a long time. This is a term I made up a couple days ago when I realized I may re-use this mechanic.
Items that use the highlight term "cursed" have extra rules explaining how the curse works. Normally a remove curse will allow you to be free of the curse's effects (including losing attunement to the item), but the item remains cursed, ready to weave its curse anew. This is how cursed items normally work in 5e; known deviations will be in the item's text.

Custom Magic Items that have been handed out:

Bracelet of Emptiness
(uncommon)
At the end of a short rest, you may cause this item to bind or unbind.
You cannot cast spells or experience joy while bound to and wearing this band, nor for five minutes after removing it.
While bound to and wearing this band, when you hit with a melee weapon attack and the weapon dice you roll produce an even number (before applying any modifiers), you deal 3 extra void damage.
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Argentic Shackles
(uncommon)
Steel with silver inlay, these shackles reduce the caster level of any creature shackled with them by 5. If the creature doesn't have levels, then if it has a CR of 5 or less it cannot cast spells or use any abilities that are magic or unusually extraordinary, such as a breath weapon, the ability to change shape, etc.
(there is a silver key that unlocks this; otherwise it is a DC 20 Dexterity check that proficiency or expertise with Thieves' Tools helps with as normal, and it is otherwise an object with 50 hit points and a damage threshold of 10 that additionally resists slashing, piercing, fire, lightning, acid, radiant, and necrotic damage, and is additionally immune to cold damage)
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Lesser Unity Bandage
(common)
Heal one hit point per minute while wearing this bandage.
When the bandage has restored 37 hit points, it becomes a nonmagical bandage. Prior to that point it cleans itself over an hour when not in use.
(these start with the ability to restore 50 hit points and can be purchased for 150 gold anywhere in Lamenciron, but cost more elsewhere as they are only created in Unity)
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Cursed Ring of Blur
(rare)
Attuned, Cursed
When attuned to this ring and you are wearing it on a finger or toe, you can, as an action or bonus action, activate it by speaking the command word.
When activated, the ring grants you the benefits of the blur spell and cannot be removed unless the finger or toe it is placed on is severed.
At the end of the round that you activated it, you take 1d3 necrotic damage. This damage can't be prevented or reduced in any way.
At the end of any other round when it is active, you take twice the damage the ring caused you last round, which can't be prevented or reduced in any way.
You can attempt to deactivate the ring with a bonus action or action. To succeed at deactivating it, you must make a DC 14 Wisdom save. On a failure, the ring stays active as your attempt to deactivate it fails.
While attuned to this ring you will not willingly take it off or lose attunement to it. Your choice to activate or attempt to deactivate it is always your decision.
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Jade Confluence Container
(very rare)
Soulbound - Nyxara
You have an empty potion bottle made of jade. If lost or destroyed, you invariably find it again, but if you sell it it is lost forever. On the first day of each month of the Elven calendar, the jade bottle has a 75% chance to fill with a Ki Confluence Potion. If poured out of the jade bottle the potion loses its magic after a few hours. (See "Ki Confluence Potion" above)
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Vial of Crimson Restoration
(legendary)
On the first day of each month of the Elven calendar this crimson glass vial has a 25% chance to fill with a Restore Potion. If poured out of the vial the potion loses its magic after a few hours. (see "Restore Potion" above)
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Vambraces of Thrown Weapons
(common)
These vambraces are made from steel bands and thick leather, and the right one has a gemsocket.
The effects of the socketed Kenda Gem are applied to any nonmagical weapon you throw.
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Amulet of Mighty Fists
(common)
This valuable amulet is made of elephant ivory and has a gemsocket in the center.
The effects of the socketed Kenda Gem are applied to any attacks you make with your body, such as natural weapons, unarmed strikes, and so on.
The gemsocket will only apply the effects of beryl, iolite, jade, and corundum Kenda Gems. So for instance, Fire Ruby III would work, as ruby is corundum, whereas Timewalk Amethyst would not, as amethyst (a quartz) is not any of the four listed materials.
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Emotionally Hardcore Invisibility Scroll
(uncommon)
You can cast invisibility on yourself with this scroll. If you are in combat with a force that cost you a lot emotionally, it is greater invisibility instead.
When used this scroll loses most of its text. You can fill in the missing text by using 150 GPs of inks normally used to add spells to a spellbook.
On a failure the materials are lost, but you can try again with new materials.
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Amulet of Split Spell
(rare)
Attuned
This silver amulet is a perfect circle about two inches across. On its front are small garnets of mediocre quality, but they are set in no discernible pattern.
When you cast a spell of first or second level that you target only a single creature with, you can select a second creature that doesn't have total cover from you, and that creature is also affected by the spell. Then roll a d4. On a 1, you can neither use this property nor can this item's attunement be changed (it remains attuned to you exclusively). These restrictions both fade at dawn.

I think I have all the custom magic items here; feel free to remind me if any are missing.
Note that as of right now, both of the magical containers are empty (the vial of crimson restoration and the jade confluence container)