Setting user permissions per post

I believe with the help of remove_post_type_support you can achieve this. But first you need to keep an user meta with the list of posts IDs he/she will be able to edit. And you can achieve this with this below function-

update_user_meta( $user_id, $meta_key, $meta_value, $prev_value )

So whenever a post will be loaded you can check the array of editable post IDs for his/her and based on that you can invoke or revoke the post type support. Have a look at the below code-

// Don't stick with the `admin_init` hook only. If it doesn't work please try with other hooks also
add_action( 'admin_init', 'codemascot_invoke_or_revoke_post_supports' );
function codemascot_invoke_or_revoke_post_supports() {
    // By setting the last parameter from `false` to `true` you will get return an array.
    // Here I'm using get_current_user_id() to get current logged in user ID.
    $editable_posts = get_user_meta( get_current_user_id(), $meta_key, true );
    // change the post type support based on your custom user permission
    if ( ! in_array( get_the_ID(), $editable_posts ) ) {
        remove_post_type_support( 'post', 'editor' );
    }
}

NB. You can store the user IDs with the permission to edit the post in post meta too. But querying a post meta has some drawbacks as post meta table usually has the higher probability of growth than user meta which may cause slow query.

This above code block is just an idea or concept which is not tested in WordPess environment. So, some important precaution are-

1. Don’t stick with the admin_init hook only. If it doesn’t work please try with other hooks also and let me know. I’ll update my answer.
2. Please read the function documentations for further info about the functions mentioned here,
3. Test the code before putting it in production.

Hope my answer helps you.