Hi Mohamed,

yes you can do that, use client object model to access the other farm.

check the following sample for the code:

https://code.msdn.microsoft.com/SharePoint-2013-Perform-eba8df54

var spUser = clientContext.Web.CurrentUser;
clientContext.Load(spUser, user => user.Title, user => user.LoginName);
List list = web.Lists.Add(...);
ctx.ExecuteQuery(); //Create the list
ctx.Load(list, l => l.DefaultViewUrl); // Request the new list's URL
ctx.ExecuteQuery(); // Get the new list'

Hi Mohamed,

yes you can do that, use client object model to access the other farm.

check the following sample for the code:

https://code.msdn.microsoft.com/SharePoint-2013-Perform-eba8df54

var spUser = clientContext.Web.CurrentUser;
clientContext.Load(spUser, user => user.Title, user => user.LoginName);
List list = web.Lists.Add(...);
ctx.ExecuteQuery(); //Create the list
ctx.Load(list, l => l.DefaultViewUrl); // Request the new list's URL
ctx.ExecuteQuery(); // Get the new list'

Hi,

In this case you can use the publishing the custom service application across different farms.

Share service applications across farms in SharePoint 2013,

and

Cross farm Service Applications Integration between two separate SharePoint far

Hi,

If you choose to work on client side, then REST API is the best option, before you need to allow the list can be accessed through anonymous enabled.

Explore this REST API in SharePoint 2013.

You can also try the SharePoint App model (Provider hosted app) to create the high trust app ( on-prem