Can I refuse to take a paternity test?

My daughter’s mother wants me to take a paternity test even though my daughter is 5 and I’ve been in her life since the day she was born. I’m pretty sure she’s mine but what if I take the test and she isn’t? Would I still have rights to visitation with her? I think my ex is doing this now because she recently asked me to pay more child support and I told her I couldn’t. I just can’t afford more right now. She’s mad and I think she’s trying to get back at me. Can I refuse to take the test on the basis that my daughter only knows me as her Dad and I don’t care what the test says, I am her father? If I have to take the test and she isn’t mine, can my ex still come after me for more child support?