I want to open Custom WebPart on click of "add new item" link (as shown in above image) in SharePoint list Programmatically.
You can edit the default new form.
- Go to list ribbon and click on Form Web Parts. From drop down click on Default New Form.
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This may help sharepoint.stackexchange.com/questions/163470/… I don't work on O365 so not sure whether this link will help you or not. – P S Apr 25 '16 at 5:50
This is possible by adding a custom action that can be to the Style Library. You would need to design your custom form programmatically in this custom action - JavaScript file and associate to this list.