For Bukkit plugins to work with modded servers you need to have KCauldron installed on your server.
I have installed KCauldron 1338 this will allow you to install MC compatible 1.7.10 plugins.
Here's a quick step by step guide.
- Discover which version of Forge your server is running by clicking the Files > Config Files navigation
- Search for "Version" in the file field, hit return to filter https://gyazo.com/b794a2767021604025ef5c41a0bda071
- Click the "Version" link to show you the file content
- Look for the jarVersion, which has the version "forge-1.7.10-10.13.4.1492.jar". The 1492 is the part you are interested in, take note of this https://gyazo.com/dee26f086b992af5ab1ade16363eb4c6
- Now go back to your server view and click the "Unlock Change Server Jar"
- Scroll up the list and find the KCauldron version which is either or greater than the version in the "version" config file, select is then click save
- Restart your server and KCauldron will automatically be installed.
This may not work 100% of the time due to certain mods being incompatible with KCauldron, the main culprits are MobiusCore and Opis.
If these mods are crashing the server follow this guide on how to disable mods https://stickypiston.co/account/knowledgebase.php?action=displayarticle&catid=11&id=84