.003 pistons/rings were available from OEM manufactures of various engines to correct a minor problem in the bore.
As the engines aged they were discontinued,
with .010 being the first oversize.
All that said it is was acceptable to use a std ring set on a .003 piston, if the .003 rings were not available and the bore was good.
But usually by the time the .003 rings are worn out, so is the bore and it needs to go to .010 oversize.
Also,
It was not unheard of to put .003 oversize rings on a std piston (when the rings were available) and filed to give the correct end clearance at the tightest point in the bore which was most always at the bottom of the travel.
Fix your head gasket problem as mentioned and you might not need to go with a rebore and new piston/rings.