I recevied a 1099c for my deceased mother,will I have to pay taxes on this debit? This was retail credit card debit.There is no probate, her house was in a trust or title to her living trust and since has been sold.

No - you personally have no responsibility to pay your deceased mother's taxes. If you are the executor of her estate (are you?) then one of your repsonsibiities is to file her final income tax return, and this 1099C would be included in that filing along with her income, deductions, etc. If taxes are owed they would be paid out of the estate's checking account, just as her other remaining debts are paid.