normal quest for rider ascension mats?

if you use this site to search for the material
https://grandorder.gamepress.gg/item/rider-piece
you can actually know where the best drop location is.
https://grandorder.gamepress.gg/item/rider-monument
AMAJING RIGHT?

https://docs.google.com/spreadsheets/d/1_SlTjrVRTgHgfS7sRqx4CeJMqlz687HdSlYqiW-JvQA/view
That's the spreadsheet for the drop rates, and oh, one thing a veteran should know is that unless you need one or two it's better to simply wait for the events as the drop rates...are abysmal and totally hopeless unless if you have EX luck.

Wait for the event and/or just do the daily for it. The droprates for monuments and pieces outside of dailies is abysmal

You mean the silver and gold monuments?

Their rate in Rider weekly Chaldea Gate is not that consistent, but outside of it they are abominable.

Do dailies, and do event shops. Well, the next one wont have rider ones (just caster, lancer and saber, I think...), but Nero Fest probably will have them.