You can only be a non-relative dependent if you meet all the requirements under the Qualifying Relative rules.
To be a Qualifying Relative -
1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,300 (social security does not count) in 2021
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.
The child may qualify him for HOH but you do not. And if you work then you may choose who will claim all of the child related benefits so neither of you should file until a course of action is decided upon using all the facts on hand.
What if we have a child together, under the age of 5?
First, to be a dependent as a non-married, non-relative, you must live in his home for all 365 days of the year, and he pays more than half your support, and your taxable income is less than $4300.
However, if your relationship is illegal under state law, you can't be a dependent. This is a more rare objection these days, but if your state has a law that makes it illegal for a married person to share a home with another person who is not their spouse, then you can't be claimed as a dependent.
He may claim his biological child as dependent even if he can't claim you, but having a child together does not change the rules on whether or not he can claim you.