The "Mismatched Mod Channel List", in simplicity, means that the mods on your client (your local installation of Minecraft) and the server are not the same. There are many potential causes for this condition, but we'll mainly focus on what to do in the instance that you encounter this error with this guide.
The error will typically show as one of two splash screens, one being just an error like so:
Or one that shows each mismatched mod:
The Solution
Because the problem lies in the mods between your server and client, the solution is simply to verify that the two lists match up. If you're running a modpack hosted from CurseForge, the easiest way is to ensure that the modpack versions are the same, as shown below:
In this instance, my client has v36 of BMC4 installed, but the server is using v41. Because the versions are different, I will not be able to join the server, as the mod lists will not match. To fix this, simply navigate to CurseForge and install the right version!
Manual Installs
If you have installed a custom modpack manually, it can sometimes be troublesome to locate what mod may be missing if Minecraft does not give you an exact list of missing or mismatched mods. The easiest way to resync your mod lists is generally to either reupload your mods to the server, or download the mods from the server onto your mod list. For the latter:
Navigate to your server's file manager
Select the Mods folder, then press Archive
Locate the Archive file, then download it
This will give you an exact, zipped copy of the server's current mod list. From here, you will want to replace your local mods folder with the contents within the archive. For this guide, we will assume that you used CurseForge to make your modpack.
Find your Mods folder
In CurseForge, right-click on your profile and click "Open Folder"
From there, you will replace the profile's mods folder with the mods folder from your server. You'll want to use 7Zip, WinRAR, or Windows' built-in features in order to extract the archive file in order to replace this folder. In this case, I'll use WinRAR.
Once it's complete, your lists should be synced up once again! If you're still having trouble, reach out to us through LiveChat and we may be able to assist further!