This question has been asked before here. You need to tell us what country you are living in (I suspect it is the UK).
If it is. Despite what you may have heard (or read in the Daily Mail), income support is not withdrawn from people who really need it. If your partner visits you occasionally and "stays over", that is not relevant.
If you are actually living together (which I guess is a subjective judgment based upon who buys the food, pays the bills, and what proportion of the time you spend together) then the authorities are less inclined to be helpful.
The very fact that you are living with your parents and your partner just "visits" is also probably helpful to you.
This all depends, of course, on whether your words "I am with my child's father but we don't live together" are completely accurate.