Solita in Spanish, literally means "little loner". i.e. "Ana está solita" translates to 'Ana is lonely'. "Solita" is very much used as a caring way , referring to lonely girls. It comes from the word "sola" (alone) with the "ita" suffix to make it a diminutive form. I never heard of Solita being a pet form of Soledad, but hey... that's optional.
"Solisita", the way you spelled it means nothing at all. Little sun would be "SOLECITO" as the sun is a masculine, diminutive word in Spanish, there forth it ends in a "O" and has the "ito" suffix in it. Little sun can also be "SOLCITO", no "e". Thus and finally, SOLECITA would be a feminine version of a name meaning "little sun".