Were all the tires BF goodrich on mopars or did they change to the Goodyear tires later in production?

BF Goodrich thru 1972 (BFGoodrich had an exclusive patent on the design) - then Goodyear in the later years

So the 73-74 E body cars used the Goodyear? So it doesnt have near the value or is as sought after

B.F Goodrich space savers were E-body only and not equipped in any Mopars that I am aware of after 1971.
72-74 E-body utilized a full size spare.
In the mid 70's F-78-14 Goodyears were in the trunks of Aspens, Volare's and Cordoba's.
People regularly claim and try and pass off the Goodyear F-78-14 as Cuda, Challenger spaceaver spares.

You can thank Galen Govier for that, he listed the the Aspen space saver wheel number as being correct for 70-71 E-Body Space Savers.

April 18, 1977 Aspen SpaceSaver Spare

I have a tire that has never been mounted is why I am asking. So it would be for a Aspen then?

If it is an F-78-14 Goodyear, it would be correct on that 2944250 rim Snoopy shows, if you are not concerned with date codes, and would be right at home in the trunk of an Aspen.
Bear in mind, as with the B F Goodrich spacesaver tires, the same in Goodyear were used by a variety of other car manufacturers GM and Ford included.

It is a F-78-14 Goodyear. I just went and looked. So it is not for a mopar then