broken screw on lock set

[ted h]

Does anyone have experience with taking out a broken screw head that broke off in the open hole side that accepts the dead bolt lock? The screw broke off in the hole and is very small about 8/32 and is not east to get at and the bracket does not appear to be removable to work on it. Does Jayco make special screws for this I am not finding a match at the hardware store. Thanks, TED