essentially I have to make use of the scripts at verify.php. however, if I navigate to mysite.com/verify.php, wordpress page turns up and throws 404.
I have to send AJAX publish for this file from jQuery within the primary wordpress index page.
In addition to later on I'll have more somescript.php to load via URL and that i need wordpress not to throw 404.
You may create a custom page template. Inside the custom page template you can your personal php code.
Before anybody can answer your question, please verify what's "verify.php", could it be personal files that you simply upload to /[your-wordpress-folder]/ or perhaps a custom page template ?
maybe his can help you :