my sons dad texted me today and said “I need a test to make sure he’s my kid since you won’t let me…

my sons dad texted me today and said “I need a test to make sure he’s my kid since you won’t let me see him” and I told him okay but this really pisses me off because he’s making it seem like I’m not letting him see the baby because I’m not sure he’s the dad and because I’m still “mad” about him cheating. When in reality my doctor said he doesn’t need to leave the house unless necessary for the first 6 weeks and I don’t feel it’s necessary just so the baby can go meet his family? My mom has opened our home to them to come visit with the baby despite everything that happened with his mom not giving me the gifts she bought my son and them making me feel unwanted at their home. So like I don’t understand where this is even coming from?? I also set it up for the paternity test to happen next week with a time and date and after I told him the price he says “well nah it’s okay I was just kidding” like nope. I’ll just go ahead and pay it because I’m not dealing with this later on, months from now when he’s mad about something and he uses the whole “he’s not mine” to get back at me. He doesn’t realize how that makes me look like why did you even sign the birth certificate if you felt this way? I’m just over all of this tbh... one minute he’s sending me text wanting to make things right and be a family next minute he’s on social media saying he’s tryna get his “dick wet” I would never keep my son from his dad because of my own personal reasons but I just don’t want him around me at all. It’s getting to a point where I don’t even wanna see his face. I’m really starting to hate him