Error: Syntax error. Missing ')' on Validation rule

Please try the below

AND(
TEXT(Case_Type__c) ="Software Issue",
TEXT(Type) <> "Markes Software",
TEXT(Type) <> "Third Party"
)

You could alos use CASE function as below to make the formula more efficient i.e. not repeatedly referencing the Type field in the formula

AND( 
TEXT(Case_Type__c) ="Software Issue",
CASE(Type,
"Markes Software",1,
"Third Party",1,
0)=0
)