BA should not permit you or anyone in your booking to sit in an exit row unless all members of your party are eligible to sit there.

If your son is age 12 or older and his autism does not prevent him from performing exit row duties, then all of you may be seated in an exit row and pay for those seats. On the other hand, if your son is <12 or his autism prevents him from performing the duties required, none of you should be permitted to sit in an exit row whether paid or not.

You have a choice to make here and it should be based on your son's needs and capacity, not on whether you might get a better seat. In the event that something goes wrong, this comes down to safety. Additionally, if his condition is self-evident, you may all find yourselves reseated at the gate or onboard.