Search for fiscal quarter and year

Are the numbers (1, 2, ... 11, etc) in the headers too?

Assuming they are not, and that you just are indicating to us the column numbers,

then something like:

=SUM(J2:INDEX(J2:N2,MATCH(A$1&" "&YEAR(TODAY()),$J$1:$N$1,0)-1))

this will sum the values in row2 starting from J2 and ending 1 column before the indicated quarter in A1 and current year.

formula can be copied down to get sums of next rows...

See attached.