When a god falls victim to temptation and has more "intimate" relations with a mortal, the offspring is known as a "Demigod". With strengths representing their godly heritage, a Demigod typically doesn't age at a normal rate, and is more powerful than the average mortal could ever be.

Demigod Traits

Ability Score Increase

Based on your godly parentage, you can increase one of your ability scores by 3.

Age - Immortality

Demigods reach maturity based on their mortal parent's race. They find old age to come much later than normal, typically living beyond 1000 years.

Alignment

Your alignment will usually match the alignment of the mortal who raised you. This, typically, is in contrast to the alignment of the god who fathered/mothered you.

Speed

Your base movement speed is 30ft.

Size

You are considered to be medium sized. Your physical attributes will usually mirror those of your mortal parent, with your god-like abilities lying beneath the surface.

Natural Linguist - Language

You have a way with languages and can learn any 3 that you so choose, in addition to already knowing Common.

Planar Adaptation

Mixing the blood of a god with the blood of a mortal leaves the offspring strangely malleable. When you leave your home plane of existence for another, your body quickly adapts. After taking a short rest there, your physical form becomes ideal for survival on the plane.

For example, if you travel to the elemental plane of fire, you have resistance to the incredible heat that would bring on quick exhaustion. If you travel to the elemental plane of water, your lungs can adapt to be able to breath in the oxygen from the water as if you had gills. 

This extreme effect only takes place if you're negatively effected by the plane's nature.

(This ability is all built around DM's discretion.)

Brash and Impulsive

The blood of the gods running through your veins is quick to boil.

You get a +3 to Initiative.

True Seeing

You have the natural ability to see past deceptions and falsehoods directed towards you. You can gain the benefits of the True Seeing spell for 1 minute. You can only use this ability once before needing to take a long rest to do it again.