If a creature has spell resistance and casts a spell, would a character casting counter spell have to overcome the creatures spell resistance to disrupt the spell?

Not sure if you intended the Abjuration Wizard's "Spell Resistance" or general "Magic Resistance" but -
Spell Resistance:" Starting at 14th level, you have advantage on saving throws against spells. Furthermore, you have resistance against the damage of spells."
Magic Resistance: "You have advantage on saving throws against spells and other magical effects."

So the question is "Where is the saving throw against Counterspell?".  Answer is there isn't one.  Either "Counterspell" is cast at a higher level and auto-succeeds or the caster of "Counterspell" is rolling an ability check against DC10+spell level they're trying to disrupt.  There's also no damage.  So whatever the case, I don't see an impact on Counterspell.

Another noteworthy piece of information that could relate if others have more information I've missed though -
From Jeremy Crawford: "Counterspell targets a creature casting a spell, no matter the source of the spell (the creature, an item, etc.)"