Does it depend on how fast you want your transaction completed? i.e, if I try with a specific amount it would be slower in the day than at night. Or is there an amount that would be too low to get a transaction completed?
This study shows that majority of miners are situated in countries using 'UTC' timezone or a very close time range.
The study doesn't show where majority of miners are... it's suggesting that people who transact are generally living closer to UTC/greenwich, that is, in Europe. But this assumes most Bitcoin users make transactions during daylight hours or working times. It's just a guidance, I've never noticed any real difference, feels random to me.
Also, how fast you want your transaction completed will always determine how much you want to pay in comparison to how much others are paying at the same time you transact.
While average fees have been very low for many months (and getting lower), you should still always check what the queue looks like and use estimates to determine a suitable fee. Personally, I've been just paying 1sat/byte fees for everything - they confirm within hours, if not within blocks. And if I need it urgently, RBF default on all my txs mean I can just pay a higher fee.
Lots of guidance about estimating fees. You can google.
1 example here to start off, but you can find better ones and make your own estimation.