Good day Tooz, benvenuto to the forum!
The two sources I have that address the fighting on Corsica in 1943 are:
Le operazioni della unità italiane nel settembre–ottobre 1943. 1975. This volume was published by the Italian historical office and covers all the theaters during that time frame. Due to that broad coverage, its discussion will be very general and usually at a high level.
Le operazioni della unità italiane in Corsica nel settembre–ottobre 1943. 1987. This volume was assembled by the Associazione Nazionale Combattenti e Reduci and does contain a lot of material. I have not delved deeply into the book, so not completely familiar with all that it offers.
Can you provide a bit more detail of the type of material you are seeking?
Pista! Jeff