Trae Tha Truth says his baby mama tried to teach their daughter he was her enemy ... but now he has full custody of their kid, he's showing her how much he loves her.

The Houston rapper tells TMZ ... his ex, Heather Cuevas, manipulated their daughter Truth into thinking her father wanted nothing to do with her ... but he says that couldn't be further from the truth.

Trae and his lawyer, Stephanie Proffitt, claims Heather's been making a string of false claims against Trae ever since their kid was born ... hoping to make something stick.

There was even a GoFundMe started by Heather that Trae and his attorney claim was littered with false claims against him ... and the page has been taken down.

They say Trae has now been vindicated -- because Truth is finally under his care.

As we told you ... Trae and Truth were reunited earlier this month at the U.S.-Mexico border in California after she had been missing for months ... and Heather was arrested for child endangerment.

Trae says Heather was trying to flee to Mexico with their kid ... but now Truth is living with him and doing well, all things considered.