Jack Avery Seeks Restraining Order Against Gabbie Gonzalez, Wants Custody of Kid

Jack Avery says his ex, TikTok influencer Gabbie Gonzalez, is being accused of conspiring to hire a hitman to kill him ... and now he's seeking court ordered protection from her and sole legal and physical custody of their daughter.

The former boy band singer beelined it to court Tuesday and filed for a temporary restraining order against Gabbie, who was arrested Friday as part of an alleged murder-for-hire plot.

Jack claims the FBI told him Gabbie, her father Francisco, and her friend Kai Cordrey, conspired to hire a hitman to have him whacked ... and now that she's been busted, he wants Gabbie nowhere near him or their 7-year-old, Lavender.  He says having sole custody rights would allow him to get a therapist for the kid to help her process everything.

In the docs, obtained by TMZ, Jack says Lavender was staying with a foster family after Gabbie was arrested Friday ... and he says he flew up to Northern California to take care of her. When he arrived, he says he was told Lavender made comments blaming him for his mom's arrest, and he alleges Gabbie has been trashing him in front of their kid.

Jack says since Gabbie's arrest, her family has been blowing up his phone demanding to know where Lavender is ... and he says on Saturday, two of Gabbie's friends came to his house and started banging on the front door, looking into his Ring camera and telling him they could "do this all day." He says he doesn't feel like he and Lavender are safe in his home.

What's more, Jack says Gabbie whisked Lavender around the world before her arrest, refusing to tell him where they were traveling. He says he didn't know they were in NorCal until Gabbie was arrested.

Jack even says the FBI warned him 5 years ago it was not safe for him to be around Gabbie ... but he says he wanted to see his kid and "had to learn to manage my own fears and anxiety" during custody visits and exchanges.