Maximum No of Free account on this Iphone

As I understand it you are limited to ten devices for one Apple ID.

View and remove associated devices in iTunes - Apple Support

This has nothing to do with iTunes, as the above post implies. Create a "new" Apple ID using a computer, you'll then be able to use this ID on your phone. There is no way to bypass the three account limit on an iPhone, unless you re-use one of the three ID's that were previously used.

mail4ayaz wrote:

Hello

I want to open My Apple Id on My Iphone but when i Sign in i Cloud there i found error Maximum No of Free account on this Iphone

That message refers to the number of iCloud accounts that can be set up on any one iOS device.

I'm guessing that you bought the phone second hand and there have already been 3 iCloud accounts set up on it. It has no bearing on Apple ID or iTunes accounts. Apple limits each device to 3 free iCloud acounts only. You can erase the device over and over again and it will not change that fact, this is tied to the device itself, not your Apple ID.

You can set up an iCloud on another device, then sign out of the iCloud account on the phone, then sign in with the newly created account from the other device.