Talk to the folks at your sequencing core. There are quality control steps, but really no such thing as "positive" or "negative" controls in a Nextgen sequencing run.

You may understand the NGS analysis in a slightly different way. Before you pay the expensive cost, you had better consider your analysis plan more deeply. NGS does not require posi & nega controls, but if you want to find some variants in cancer tissue or something, you should have the reference DNA, like, DNA from the patient's blood. Without this, it is very difficult to do the variant calling.

As far I know, if you are sequencing, the most probable situation is that, or you know predicted sequences or you know sequences of the same genes in other model animals. So the positive control does not have sense to me in sequencing a gen. And the negative either. Different thing could be if you know the sequence and you would like to confirm or demonstrate the presence of the gen in different tissues. In this situation I would use specific primers and Real Time PCR, and positive and negative theoretical controls of tissues in whcho you have some data to assume thta the gen is there and not. But this is not sequencing.