Edit: Precious Conjunctions (and their current owners) now in PAR's post, followed by a post with other custom items that have been handed out.

Precious Conjuncts:

[K01] Shining Lucid Beryl (common): Nyxara : Session 1
[K02] Perfect Quartz (uncommon) : Nyxara : Session 1, from Isaï Memory soldiers
[K03] Perfect Pure Corundum (uncommon) : Geddreng : Session 3, from slain kunoichi, upgraded Session 4
[K04] Daring Heliodor I (rare): Skattebo : Session 4, from Bearded Demon's stolen glaive
[L01] Impulsive Lustrate Star (rare): Cyndra : Session 4, from Bat Demon

Custom Magic Items that have been handed out:

Bracelet of Emptiness
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.

Argentic Shackles
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)

Lesser Unity Bandage
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)