This paper is divided into two logical parts. In the first part of this paper, we prove the following theorem which is the q-analogue of a generalized modular Ray-Chaudhuri-Wilson Theorem shown in [Alon, Babai, Suzuki, J. Combin. Theory Series A, 1991]. It is also a generalization of the main theorem in [Frankl and Graham, European J. Combin. 1985] under certain circumstances.Let V be a vector space of dimension n over a finite field of size q. Let K = {k1,…,kr}, L = {μ1,…,μs} be two disjoint subsets of {0,1,…,b-1} with k1<….< kr. Let F = {V1,V2,…,Vm} be a family of subspaces of V such that (a) for every i ∈ [m], dim(Vi) mod b = kt, for some kt ∈ K, and (b) for every distinct i,j ∈ [m], dim(Vi ∩ Vj)mod b = μt, for some μt ∈ L. Moreover, it is given that neither of the following two conditions hold:(i) q + 1 is a power of 2, and b = 2 (ii) q = 2, b = 6. Then, (formula presented) otherwise, where (formula presented) In the second part of this paper, we prove q-analogues of results on a recent notion called fractional L-intersecting family of sets for families of subspaces of a given vector space over a finite field of size q. We use the above theorem to obtain a general upper bound to the cardinality of such families. We give an improvement to this general upper bound in certain special cases. © The authors.