extent of the man's right to the woman whom he never married

Hello,
I had a former relationship and that gave me a 6yo son. We never got married as he still has a previous marriage from her former partner which was not yet concluded by the court. We split sometime in 2014. Just mid last year, I found a new partner, he is a transman, and he wanted us to live together. I am hesitant because of my son. I am not sure if my son's father will have any chance to get the custody of my child if he knew about my current relationship.
I am almost fully supporting my son, the father gives only Php10K a month, and I gave him visitation rights every saturday only due to busy schedule at my son's school.
What is your opinion about my situation and are there any possibilities that he will claim for my son's custody?

Thanks

i don't think this will be a case unless he will make it appear that the child is affected by the situation and the environment you provide is toxic for the child.