What is a $D^{0 \ast}$ meson? What are the quark contents of $D^{0 \ast}$ meson? 
How to distinguish between $D^{0 \ast}$ meson and $D^{0}$ meson as I guess both have same quark content.
 A: There are many excited states of flavoured mesons ($K$s, $D$s and $B$s), which are identified by their mass, spin and parity. The mass is usually written in parentheses in MeV (omitted for ground states), the subscript contains the spin (and the lighter quark if it isn't a $u$ or $d$), and the superscript contains the charge and sometimes a star. 
The star tells you what the parity is in relation to the spin: positive for even spin, negative for odd. If there's no star then it's the other way around.
From the PDG naming scheme for hadrons in the section on flavoured mesons:


  
*If the spin-parity is in the "normal" series, $J^P = 0^+, 1^-, 2^+,...$, a superscript "$^*$" is added.
  

A: The standard model of physics has as building blocks of hadrons and hadronic resonances the quarks. The quarks have flavors that characterize them and the various ground state quark combinations giving rise to a resonance have been given various alphabet identifications. Excited states of that specific combination gets a star, which denotes that it is not at the ground level and will decay to or has the same quark content as the ground state. (As these are strong interactions  they happen very fast) .
The D notation carries charm and anticharm quantum numbers and the ground state is 

Excited states of the same quark content will be denoted with a * and will be of a higher mass than the D, with appropriated quantum numbers. It is analogous to the excited states of the hydrogen atom, except these are of the strong and not the electromagnetic interaction.
The problem with the notation gets out of hand, because of all the possible resonances which are fitted to be classified as D resonances . Have a look at this link. . You can search for specific states here .
