I am using q parameter inside Gmail API request. It is documented that it accepts same queries as Gmail web app.
I used this query: newer_than:1480338055000
However, it is not showing any messages (tested it on both API calls and Gmail client)
However older_than: accepts unix-like timestamp.
I am currently in GMT+1 timezone if that would matter.
Why doesn't it work properly and what are other alternatives to query messages that appeared after specific time (should be precise at least by 1 hour)
You can use before or after with second accuracy. Just give seconds since the epoch:
after:2016/01/01 <=> after:1451606400