I did not sell my timeshare. I paid a company to take the timeshare since I couldn't sell it. It is a loss. how do I claim it.

Timeshares can be considered a second home in order to deduct any mortgage interest and property taxes.  Personal gains are taxable but personal losses are unallowable. Unless you received income from renting your timeshare out and reported rental income, the timeshare is considered personal for tax purposes.