How can I add an argument in the URL that link from a content
You could add the Title ID field to your view, exclude it from display, move it above the link, enable rewriting on the link field and write the link format you want, including the Title id.

Edit following the follow-up question: 
Well, in my opinion, you shouldn't have to put the Title id in the URL at all. What I wrote above solves your specific problem but, really, I think you should do things differently and thus wouldn't have this problem or the follow-up one.

Link to node/quoteid and load the Title node by looking at field_title_id (replace by the actual field name). You can do that loading in hook_preprocess_node by calling node_load($node-&gt;field_title_id[LANGUAGE_NONE][0]['nid']) from there you can either render the whole title node (node_view) or just get one field and send it to your template.

Basically, the Quote->Title relation is in the database, there's no reason you should have to express it in the form of a URL. The reverse would make sense, if you had a Title page where you want to show a single quote.

Second edit following the second follow-up question:

To display all other Quotes linked to the same title you could create a view with Title ID as a contextual filter. You can render the view manually in your template, passing it the Title ID. That'll display all quotes, including the main one displayed in that page. You probably want to filter that one out one way or another.