Is there any distance course in AU to finish my BE after Diploma?

At present, there is no feasible option nor you must do as it is a practical subject. AICTE stressed on its practical exposure so it restricted BE to full-time non-distance study.

AICTE doesn't permit any distance learning programmes. So, here you have an option to pursue AMIE where you get a technical B.Tech degree (even AMIE isn't clear and the decision will be maximum revealed in July 2019).