I was thinking of going back back to your formula later after I learned Arvi's. I changed the givens in the OP by populating E1 to E12 with the months of the year. In A1 to A12, your formula returns the value of $F$1 on January, April, July and October, all the 1st month of every quarter. In B1 to B12, I would like your formula to return the value of F1 when the months are on the second months of the quarters, like Feb, May, Aug and Oct. In C1 to C12, the Value of F1 should be in the Mar, June, Sept and Dec.
Obviously, English is not my first language so I hope I did not make the problem more confusing.
I am using my cp, my laptop could not connect with its hotspot so I couldn't attach a file.
Thank you.