extern int var;
static int var; /* Undefined behaviour */
C11, §6.2.2, 7 says:
If, within a translation unit, the same identifier appears with both internal and external linkage, the behavior is undefined.
Note that if an prior declaration of an identifier is visible then it'll have the prior declaration's linkage. C11, §6.2.2, 4 allows it:
For an identifier declared with the storage-class specifier extern in a scope in which a prior declaration of that identifier is visible,31) if the prior declaration specifies internal or external linkage, the linkage of the identifier at the later declaration is the same as the linkage specified at the prior declaration. If no prior declaration is visible, or if the prior declaration specifies no linkage, then the identifier has external linkage.
/* 1. This is NOT undefined */
static int var;
extern int var;
/* 2. This is NOT undefined */
static int var;
static int var;
/* 3. This is NOT undefined */
extern int var;
extern int var;