Petrifying Gaze. When a creature that can see the medusa's eyes starts its turn within 30 feet of the medusa, the medusa can force it to make a DC 14 Constitution saving throw if the medusa isn't incapacitated and can see the creature. If the saving throw fails by 5 or more, the creature is instantly petrified. Otherwise, a creature that fails the save begins to turn to stone and is restrained. The restrained creature must repeat the saving throw at the end of its next turn, becoming petrified on a failure or ending the effect on a success. The petrification lasts until the creature is freed by the greater restoration spell or other magic.

Unless surprised, a creature can avert its eyes to avoid the saving throw at the start of its turn. If the creature does so, it can't see the medusa until the start of its next turn, when it can avert its eyes again. If the creature looks at the medusa in the meantime, it must immediately make the save.

If the medusa sees itself reflected on a polished surface within 30 feet of it and in an area of bright light, the medusa is, due to its curse, affected by its own gaze.

Spellcasting. The Yuan-ti Medusa is a 5th-level spellcaster.  Its spellcasting ability is Charisma (spell save DC 15, +7 to hit with spell attacks).  It regains its expended spell slots when it finishes a long rest.  It knows the following sorcerer spells:

Cantrip (at will): Fire Bolt, Friends Message, Poison Spray, Ray of Frost

1st Level (4 slots): Charm Person, Disguise Self, Magic Missile

2nd-Level (3 slots): Blur, Invisibility, Spider Climb

3rd-Level (2 slots): Counterspell, Melf's Minute Meteors

Legendary Resistance (2/day). If the yuan-ti medusa fails a saving throw, it can choose to succeed instead.

Multiattack. The medusa makes either three melee attacks--one with its snake hair and two with its shortsword--or two ranged attacks with its longbow.

Snake Hair. Melee Weapon Attack: +5 to hit, reach 5 ft., one creature. Hit: 4 (1d4 + 2) piercing damage plus 14 (4d6) poison damage.

Scimitar. Melee Weapon Attack: +5 to hit, reach 5 ft., one target. Hit: 5 (1d6 + 2) piercing damage plus 8 (2d6) poison damage

Longbow. Ranged Weapon Attack: +5 to hit, range 150/600 ft., one target. Hit: 6 (1d8 + 2) piercing damage plus 7 (2d6) poison damage.

Tail Lash. When hit by a creature within 10 feet of it, the yuan-ti medusa may use its reaction to lash out at the triggering creature.  The target must make a DC 13 Dexterity saving throw or be knocked prone.

The Yuan-ti Medusa can take 2 legendary actions, choosing from the options below.  Only one legendary action option can be used at a time and only at the end of another creature's turn.  The medusa regains spent legendary actions at the start of its turn.

Constrict. The medusa targets a creature within five feet of it, that creature must make a DC 12 Strength saving throw or be grappled and restrained. The yuan-ti medusa cannot constrict another target while holding a creature in this manner. The target may use its action to repeat this save on its turn to try and break free.
Move. The yuan-ti medusa may move up to its speed.
Attack. The medusa makes one weapon attack with either its scimitar or its longbow.

Lair Action. On initiative count 20 roll a d6.  On a roll of 1-2, nothing happens.  On a roll of 3-5, two of the stone statues in the lair are animated into Stone Cursed.  On a roll of 6, three stone statues are animated into Stone Cursed.
        No more than four Stone Cursed statues may be animated at a time.