The stats will change depending on who the heavenly parent is 

When you roll a 1 on an attack roll, ability check or a saving throw you can roll again

Your connection to the divine is strong and its strength gives you away to others. Creatures with the celestial, fey or fiend creature type as well as creatures with a divine connection know you are a demigod. A successful intelligence (Religion) check to discern who your godly parents is. 

In addition, if you are of a divine class such as a cleric, you must choose the domain of your godly parent.

You are innately better than others in areas pertaining to your godly parent’s divine domain. Choose an option from the Divine Domain Ability Score Increases that pertains to your godly parent’s domain.

Your godly parent has dominion over a specific portfolio. Choose an option from the Divine Portfolio Traits that pertains to your parent's divine domain. This must be the same as the option you picked for your divine domain trait.

Godly Parentage. Unswerving of will and unassailable of mind, you have advantage on saving throws against being charmed and frightened. In addition, you cannot be aged magically.

Even though it is your godly parent that makes you special, you still have a mortal parent. While you don't receive any of the racial traits that your mortal parent has. Your mortal parent must be humanoid and you physically resemble that race in its most epitomized form.

Demigods have a limited ability to sense events involving their portfolios. You automatically sense notable events and minor events within 5 miles that involves your portfolio. When a demigod senses an event, it merely knows that the event is occurring and where it is. The demigod receives no sensory information about the event.

For example, if a demigod of the nature portfolio was within 5 miles of a forest fire it would become aware of it and where it is happening. If it was 10 miles away it wouldn't have any idea but if that forest fire broke the seal on an ancient evil that their godly parent or some other nature god locked away you would become aware of it as well as the location of the site.

You can speak, read and write Common and all demigods have the innate ability to speak, read and write Celestial. Whether they discover this by meeting an angel or when a traveling aasimar got a peek at their scribbles as a child is, it is ultimately up to you. Celestial as a language sounds like a heavenly choir when spoken, and is written with a grace and fluidity that no mortal language has replicated.