Since you are not legally married you can only file your tax returns as Single.
However, depending on who provided over one-half the cost to maintain the home, they may be able to have Head of Household filing status if they claim the child on their tax return.
See this for head of household - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualify-head-household...
