Disable GPS, mobile data, wifi, bluetooth, auto rotation, auto brightness
Root your phone, install greenify and hibernate all user apps.
Remove unnecessary apps from startup using ES Task Manager
While charging, don't unplug the phone until its completely charged and don't plug it back before battery reaches 15%
Report back with new results.
Still, if nothing changes, get Yu Yureka. It is giving 1.5-2 days of battery life with 8-9 hours of on screen time.
btw, how did you bought a
Redmi Note 3?

Xiaomi hasn't even produced it yet.