Why a star above the head?

[Paul B4]

What is the meaning of the start above Vetranio on the reverse?

While we are at it, what are the meanings of the A and Δ (delta) across the field on the reverse?

Thank you!

[Jochen]

I think that these are series characters.

Jochen

[Paul B4]

Thank you. 
What are "series characters"?

[Jochen]

Roman coins were often stuck in successive series. To distinguish these series, they were marked with letters or signs. 

Best regards

[SC]

That star is part of the design and doesn't change like the file dan exergual marks do.

It is uncertain what it means or who is on the reverse.

The type was struck by Vetranio in his name and Constantius' name and later by Constantius II for himself and Gallus.

It is based on a PRINCIPI IVVENTVTIS type of Constantine from 307.  Vetranio changed the two military standards to labarums (with chi-rho).  He was likely implying loyalty to Constantine's "house".

I believe that the two labarums refer to the two armies - Vetranio's and Constantius'.  Whether the figure was meant to be Vetranio, Constantius, Constantine or be ambiguous is unclear.  Personally I think maybe Constantine and the star represents his divine status.  The other contemporary coin was HOC SIGNO VICTOR ERIS, based on Constantine's Milvian Bridge victory, so they would match.

SC

[Paul B4]

Thank you, Shawn.
This is a big help.
I enjoy learning about the coins and, when possible, discovering the meaning of every mark. 

[Dominic T]

I read somewhere that the star is probably a symbolic of the divine bond of the emperor.
DT

[antoninus1]

Yes, maybe still a reference to Sol.

[Paul B4]

Thank you both for these perspectives on the star.