I purchased a home with another party, who can claim this home on their taxes? me or them or both?

The purchase of a personal residence is not reported on at tax return.

You can deduct any mortgage interest, mortgage insurance and property taxes paid on the home as an itemized deduction on Schedule A.  But on your tax return only the amounts that you actually paid can be deducted.

The total of all your itemized deductions on Schedule A must be greater than the standard deduction for your filing status to have any tax benefit.

Standard deductions for 2021

• Single - $12,550 add $1,700 if age 65 or older
• Married Filing Separately - $12,550 add $1,350 if age 65 or older
• Married Filing Jointly - $25,100 add $1,350 for each spouse age 65 or older
• Head of Household - $18,800 add $1,700 if age 65 or older