How to get OTG support for my rooted phone

OTG is a feature that is needed to be supported by the hardware of your phone. You cannot enable the feature just by rooting your device. Rooting gives you root permissions as far as software is concerned. USB OTG functionality is definitely a hardware based feature.
If you are sure your hardware supports the OTG function, then you may need to install a custom kernel to enable it. You can search for it over the XDA developers forum. Please note that most of the kernels and mods available on XDA are developed by software enthusiasts who are not necessarily experts in the arena. Also the mods developed may not have been tested on all devices. You need to be careful while dealing with them. Kernels are device and build specific. Of you install a wrong kernel, you may run the risk of bricking your phone. I would advice you not to indulge into it if you are not an expert in the field.
Chainfire seems to have an app for enabling the OTG service. Search for the app on Play Store. If the phone software is not providing the support for OTG, but hardware does - this could e your solution.

Some users have stated that ES File Explorer is a great tool for making use of OTG functionality even when it is not supported by your phone software. Connect any of your external drives to your phone and search for it on ES File Explorer. If the drive is recognized, it will be shown up as a separate folder. The app works even when you are not rooted.
Please note that enabling OTG on a phone that does not support is needs quite a good knowledge of software and hardware. Besides, it may or may not work. There would be the cases, wherein even if you enable the feature you may end to power the external drive using some external power, the phone may not power the drive.

If you have rooted your device already then you can use the Mods created by other companies. There are plenty of open source and closed source mods out there. To name a few - MIUI and FlyMeOS. You can pick the one that supports the OTG functionality. In theory every modern MOD does support OTG. Just make sure if that support is native for your phone. Because not all mods can make use of device specific settings and hardware.

Read a bit about their support on how the OTG support works. That way you don't have to go through the process of installing and removing that mod.

Make sure that your base device has the OTG (microUSB 2.0) standard supported. if it is earlier version then you may find that most of the mods not supporting it. Your only option in such case is to revert back to the default factory state. Because if the hardware standard is upto the old version, you can't make software to support a functionality based on updates.

Your mode of action should be finding a good Mod that supports OTG. Then install the app that allows you to verify the file transfer. So most of the file and folder explorer apps can do that. If things don't go well you can always revert back to factory setting. Keep a backup in such case.