Should one build Frost Queen's Claim or Talisman of Ascension on Janna support?

I say Talisman since Janna is more of a peel support rather a poke support. But that's just me.

If you are good you can start spell thief into frostfang, but i would not advise fqc. Sell frostfang and buy talisman when you need to. Some ad from runes, shield, and bonus dmg from thief can make for some heavy poke early. Viability depends on your skill and who the other support is.

I don't play Janna, so I can't really say too much about which one to choose, but I played against a Janna that build Talisman, stacked movement speed with all three move speed/AP items, and we literally could not catch her because of how fast she was.

Alright so that depends on your laning phase playstyle with janna:

Frost queen's claim is better if you play a more aggressive janna. The active is good for chasing down enemies. Your gold income for this item depends on you playing aggressive to proc-ing the passive "Tribute"

Talisman of ascension is great for engaging and disengaging from teamfights and provides better utility than FQC for that purpose. Ancient coin is actually a very weak laning phase item since it does not provide combat stats, only some sustain.

So if you're playing aggressive, i'd go for FQC . If you're playing more passive, ToA is better.