It’s always a tough challenge when you work within boundaries or limitations of a framework. In Shopify, you cannot create your own custom fields until the use of shopify’s advanced features. These features allow to store additional customer information in the form of notes.
Whatever information you want to get from the customers can be stored in the form of notes in the shopify backend under customer’s menu option.
In order to define and use the shopify notes, please review the following form code structure.
<input type="text" title="Please enter city name" name="customer[note][City]" value="" />
<input type="radio" name="customer[note][sex]" value="Male"/> Male <input type="radio" name="customer[note][sex]" value="Female"/>
<input type="checkbox" name="customer[note][Weekly Newsletter]" value="Yes" checked />
You can define as many customer notes you want in your form.