Can i claim my spouses child as my own if we are not married?

Yes, as a "Qualifying Relative" assuming he/she meets the criteria below.

You can claim a child, relative, friend, fiancé(e), and so on as a dependent on your 2023 taxes as long as they meet the following requirements:

Qualifying child:

• They're related to you.
• They aren't claimed as a dependent by someone else.
• They're a US citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They're under the age of 19 (or 24 for full-time students).
  • There's no age limit for permanently and totally disabled children.
• They lived with you for more than half the year (exceptions apply).
• They didn't provide more than half of their own support for the year.

Qualifying relative:

• They don't have to be related to you (despite the name).
• They aren't claimed as a dependent by someone else.
• They're a US citizen, resident alien, national, or a Canadian or Mexican resident.
• They aren’t filing a joint return with their spouse.
• They lived with you the entire year (exceptions apply).
• They made less than $4,700 in 2023.
• You provided more than half of their financial support.

When you add someone as a dependent, we'll ask a series of questions to make sure you can claim them. There may be other tax benefits you can get when you claim a dependent.