Hi, thank you for your question. Just a bit more information required to fully assist you:
-How old is the child?
-What have the arrangements been to date?
-Is he named on the birth certificate?
Thank you. Firstly, given the concerns you have raised, this is reasonable to refuse contact without there being safety provisions in place for him to have contact - which you appear to have proposed by offering contact supervised at your home.
If he pursues an application to court, the court will allocate a CAFCASS officer (a court officer) to interview both of you and carry out background and police checks on you both, and any partners or members of both your households. The officer then makes a recommendation to court about what orders should be made. The history of his partner is likely to raise serious concerns about unsupervised contact, however, the child has a right to a relationship with both their parents and therefore there may be a recommendation for there to at least be supervised contact in a contact centre.
I hope this assists you. If you found this information helpful please provide a positive rating using the stars at the top of this page. I will not be credited for answering your question without a positive rating. Thank you