For Gaya :-
1) 12314 for GAYA (arrival before 4 AM).
It is good if Seat is Available.
.
2) 12302 NDLS-HWH Raj has more Quota for Gaya than other Rajdhanis.
3)...
more... Bhubneswar Rajdhani has
.
For Patna :-
12310 for Patna (arrival before 5 AM) is
#ISO Certified Train.
It has GNWL waiting which gets confirm if booked well in Advance.
.
For JHD Jehanabad :-
More trains are available in morning from GAYA than PNBE.