How to create new permission for custom post types for doing specific tasks

Check the below code-

add_action( 'admin_init', 'the_dramatist_add_role_caps', 999 );
function the_dramatist_add_role_caps() {
    // Add the roles you'd like to administer the custom post types
    $roles = array( 'editor', 'administrator' );

    // Loop through each role and assign capabilities
    foreach($roles as $the_role) {

        $role = get_role($the_role);

        $role->add_cap( 'read' );
        $role->add_cap( 'read_{Post_Type_A_Name}' ); // Also do for Post_Type_B
        $role->add_cap( 'read_private_{Post_Type_A_Name}s' ); // Also do for Post_Type_B
        $role->add_cap( 'edit_{Post_Type_A_Name}' ); // Also do for Post_Type_B
        $role->add_cap( 'edit_{Post_Type_A_Name}s' ); // Also do for Post_Type_B
        $role->add_cap( 'edit_others_{Post_Type_A_Name}s' ); // Also do for Post_Type_B
        $role->add_cap( 'edit_published_{Post_Type_A_Name}s' ); // Also do for Post_Type_B
        $role->add_cap( 'publish_{Post_Type_A_Name}s' ); // Also do for Post_Type_B
        $role->add_cap( 'delete_others_{Post_Type_A_Name}s' ); // Also do for Post_Type_B
        $role->add_cap( 'delete_private_{Post_Type_A_Name}s' ); // Also do for Post_Type_B
        $role->add_cap( 'delete_published_{Post_Type_A_Name}s' ); // Also do for Post_Type_B

    }
}

This way you can add permission to any user roles.

If you wanna create a new role for the user who should get permission then create a new role like below-

function add_the_dramatist_role() {
    add_role('the_dramatist_role',
             'The Dramatist Role',
             array(
                 'read' => true,
                 'edit_posts' => false,
                 'delete_posts' => false,
                 'publish_posts' => false,
                 'upload_files' => true,
             )
    );
}
// Remember this must be called plugin main file.
register_activation_hook( __FILE__, 'add_the_dramatist_role' );

Then add the_dramatist_role to the previous function the_dramatist_add_role_caps‘s $roles variable like this-

$roles = array( 'the_dramatist_role', 'editor', 'administrator' );

Now the_dramatist_role will have all those privileges.

Hope the above helps.