Below are four most popular Android 7.x Nougat custom ROMs for Xiaomi Redmi 3 and Redmi 3 Pro device. To flash custom ROM on your Redmi 3 device you must have TWRP Custom Recovery and unlocked bootloader. Check out this post to find out how to flash custom ROM on Redmi 3S.
Download Android 7 Nougat Custom ROMs for Xiaomi Redmi 3 / 3 Pro
AOSP CAF Custom ROM for Redmi 3
AOSP CAF is a clean Android 7 Nougat custom ROM. Very stable ROM without any critical bugs.