laravel eloquent relationship with and where clause based on foreign column

You may try this:

$value="someName";
Project::with(['clients', 'tasks', 'status' => function($q) use($value) {
    // Query the name field in status table
    $q->where('name', '=', $value); // '=' is optional
}])
->where('status_id', '!=', '2')
->whereUserId(Auth::user()->id)
->get();

Also you may try this (It will fetch records only if the query returns name you want, otherwise none):

$value="someName";
Project::with(['clients', 'tasks', 'status'])
       ->whereHas('status', function($q) use($value) {
       // Query the name field in status table
       $q->where('name', '=', $value); // '=' is optional
})
->where('status_id', '!=', '2')
->whereUserId(Auth::user()->id)
->get();