You don't pay capital gains. You receive capital gains. Capital gain is the profit you make from selling something. You have to pay income tax on the capital gain that you receive (in most cases). So the basic answer to your question is yes, you do have to pay tax on your capital gain.
Your capital gain from the sale is your share of the selling price minus your basis. Your share of the selling price is the total selling price times your percentage of ownership. So if you own a 1/3 share of the property and it is sold for $900,000, your share of the selling price is $300,000.
It sounds like your share of the property was a gift from your parents. If so, your basis is your parents' basis for your share. If they purchased the property, their basis is the amount they paid for it (plus the cost of any improvements). If your parents purchased the property for $300,000 and gave you a 1/3 share as a gift, then your basis is $100,000.
If your share of the selling price is $300,000 and your basis is $100,000 then your capital gain is $200,000. That's the amount that will be reported as taxable income on your tax return.
If your parents bought the property more than one year before the sale, your capital gain is long-term, which is taxed at lower rates. If all of your other taxable income is less than $48,350 (for 2025) part of your long-term capital gain will be taxed at a 0% rate.
Since you never lived in the home that is being sold, you cannot exclude any of your gain from taxation.
Everything I've said applies specifically to you. It may not apply to your parents, especially if they lived in the home that is being sold. What I've said is also based on the assumptions stated. If any facts are not as I assumed, your tax might be different. The situation also might be different if one or both of your parents has passed away.
