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.
Download here: aosp-caf-n-mr1-20170330-ido.zip (375.3 Mb)
crDroid 7.1.2 Nougat Custom ROM for Redmi 3
Another quite stable ROM based on Android 7.1.2.
Download here: crDroidAndroid-7.1.2-20170415-ido-v2.5.zip (442.6 Mb)
Download Lineage 14.1 for Redmi 3 / Redmi 3 Prime
One of the best custom ROMs around at the moment. Great performance and additional features.
XenonHD 7.1 Custom Rom for Redmi 3
Android 7.1 Nougat ROM based on Cyanogenmod. This ROM comes with improved battery life, additional features, customization options and quality performance.