We broke the story ... Tameka lost an arduous custody battle last week when a judge ruled in Usher's favor, awarding him primary custody of their two young boys.

Tameka vowed to appeal the decision ... by filing a motion for new trial on grounds the judge was biased in Usher's favor.

Tameka claims the judge has a strong tie to Usher's lawyer, claiming the attorney was personally responsible for nearly half of the contributions to the judge's re-election campaign in 2008. What's more ... Tameka alleges Usher's lawyer served on the judge's re-election campaign committee.

Tameka also insists NO evidence was presented showing she couldn't take care of her kids.

Tameka also claims there was clear evidence of Usher's "past, current, and future inability" to care for the kids.