Yes. It is somewhat in between a smile and a grin.
smirk
Smiling, beaming
Wipe that smirk off your face! Please don't smirk at me.
(A smirk may be arrogant, derisive, or innocently playful.)"When the investigators asked him about the crime, the suspect gave a smirk in reply.""I swore that I would win and wipe that arrogant smirk off his face.""Seeing an impish smirk on her son's face, Mrs. Smith suspected he was up to mischief again."
To smile in an affected, often offensively self-satisfied manner
The word smirk is a noun meaning sly smile. Synonyms for the word smirk include beam, grin, leer, simper, grimace, grim, sneer, visage, and smug look.
Smirk does not have a suffix. Usually words with only one syllable, don't have a suffix.
Grin.
smirk
The prefix of the word "smirk" is "sm-" which means a slight curling of the lip, often indicating amusement or smugness.
Josh had a smirk on his face when he got a B+ on his test.
Grin or smirk
smirk
smilestilestalestarestarksharkshirksmirk
perhaps "grimace"
"Johnny had a mischievous smirk upon his face after having read his sister's diary."
Smiling, beaming