Dividing a body of ancient coinage into successive issues is always a modern construction. The issue numbers are not marked on the coins, and of course we have no literary or epigraphical evidence for how the mint divided and numbered its issues, if indeed the mint gave any thought at all to such matters. Therefore when we attribute an ancient coin to a particular issue, we should always name the scholar whose scheme we are following.
On my own arrangement of Gordian's coinage, your LAETITIA AVG N type belongs to his Fourth Issue, struck between 240 and 243. Mattingly in RIC, pp. 6-7, also says Issue 4, though his arrangement of Issues 1-3 differs somewhat from mine. I would contend that my arrangement is simpler and more logical than any that might consider this to have been Gordian's third or eighth issue!
As to officina numbers, how can we possibly know them unless they are written on the coins? Since they are not so marked under Gordian III, it behooves us to admit that we do not know how the mint numbered its officinae, and which officinae struck which types. To name officina numbers when they are not marked on the coins will for the most part be pure fantasy, a claim to knowledge that we do not and cannot possess!