the determinant is just a number. For that matter the (i,j) minor is the determinant of the matrix formed by deleting the ith row and jth column from a square matrix. So the phrase "determinant in a minor" doesn't really make sense. You would just say the (i,j) cofactor is (-1)^{i+j}(i,j) minor.

The cofactors for a 4x4 matrix will be found by taking the determinants of 3x3 matrices and in general the cofactors of an NxN matrix are found by taking the determinants of (N-1)x(N-1) matrices.