No, you do not pay a deductible amount to get another car fixed if the person whose car you damaged makes a claim against your insurance policy for the damages you caused in an accident.

If you are at-fault in an accident and the other party makes a claim against your property damage liability (this is called a third party claim) then there is no deductible amount due by either you or the other car owner. Your liability insurance pays for their damages without you owing a deductible.

If your own vehicle was damaged and you used your collision coverage then the deductible you had associated with this physical damage coverage would be due.