My child’s father and I have a notarized paper saying he pays $300 a month in support, is there any way to file for more support?
If you don't have a legal support order, you will need to file for one.  A notarized document without anything else is not appropriate or enforceable. You need a court order by a family court. You need to consult with a family attorney about the next steps about petitioning for support and this will be an enforceable order.