Finesse2tymes Accused of Making Death Threats to King's Current Guardian

2/1 -- 6/33 AM PT -- Finesse2tymes’ attorney Carl A. Moore tells TMZ … the rapper  “did not threaten the complainant in any way.  We are confident this matter will be resolved justly once the state of Texas applies the applicable law to the facts.”

Rapper Finesse2tymes has a warrant out for his arrest ... over claims he made terroristic threats against a woman with ties to his former child protégé, King.

According to court records, obtained by TMZ ... back in October, police were called to the Will Clayton Parkway neighborhood in Humble, TX ... where a woman accused Finesse2tymes and his brother of verbally threatening her outside a local smoke shop.

Per the documents, the drama stems from a custody issue involving an 11-year-old boy nicknamed "King" ... who Finesse2tymes fans will recognize as the "Back End" rapper's former mentee, who he used to care for.

Finesse2tymes and King have since had a falling out, with the woman who called police apparently acting as the guardian for the boy -- though, it seems neither Finesse nor the woman are related to King.

On the day of the alleged incident --October 23, to be exact -- the arrest warrant states the guardian and King stopped by the smoke shop in the middle of the afternoon to pick up the woman's grandchild, who she was supposed to babysit ... when King was told to go inside and speak with Finesse2tymes, who had requested to speak with him.

The woman claims King ran from the shop not long after, screaming in a "panic" ... "They trying to send me back to Memphis.”

The woman says King hopped back into her car, where she had 4 other children in tow ... and told Finesse2tymes to get away from her vehicle.

She claims Finesse2tymes ignored her request and approached the car with his brother in an intimidating fashion ... and his brother allegedly threatened to "up that fire" -- Memphis slang for pulling a gun, according to the report of the incident -- and tapped his waistband.

The woman claims she could see the imprint of the man's gun through his shirt.

Finesse2tymes allegedly made his own threats, yelling more than once ... "YOU GONNA DIE ON CAMERA TODAY." The woman then drove away from the scene.

Following this alleged exchange, the woman told cops she believes the rapper is capable of carrying out his threats ... and, in turn, fears for her life.