This cursed ring appears to be a ring of invisibility if examined, and functions as one for one week after being attuned (if unattuned and re-attuned, the week does not start over; it can 'remember' up to 30 people):

While wearing this ring, you can turn invisible as an action. Anything you are wearing or carrying is invisible with you. You remain invisible until the ring is removed, until you attack or cast a spell, or until you use a bonus action to become visible again.

After a week has passed the ring cannot be unattuned or removed, and the ring's limited sentience turns on.  It will pick the most inconvenient time to do one of the following up to once per round, with no more than 1 active at once.  These effects may give you Disadvantage on skill checks or saving throws under certain circumstances, at DM discretion:

• Create an illusion of Ulcifen next to you to scream insults at you and interrupt a long rest or distract you from delicate work, often specifically criticizing you for robbing and murdering him (the ring's limited sentience does not allow it to learn or be persuaded, so you sadly can't convince it that you didn't do this).
• Create an illusion of a demon next to you to report that they received the child souls you sent them and are grateful.
• Create an illusion of a trumpets playing and a large glowing arrow pointing to where you're hiding.
• Create an illusion of yourself over top of yourself, making rude faces or yelling out insults.
• Create an illusion of yourself over top of yourself, but naked and with unflattering changes to your physique.
• Create an illusion of a blindfold in front of your eyes, rendering you blinded unless you succeed on a DC 17 Intelligence saving throw.
• Create an illusion of bugs swarming over your body.

While the ring is unlikely to let you go unseen when you want, technically you can still turn invisible.  Note that if it chooses to create an illusion of you over top of you, you don't count as invisible for purposes of combat since enemies can accurately see where you are even if some details are different.

Notes: Invisible, Deception, Cursed, Jewelry