Put the right man "on the right job" or "in the right job"?

In the US, on the job refers to a task assignment, while in the job refers to a job slot placement. You choose the one that means what you intend. It might be different in Britain.

Both are correct, but the meanings can be quite different:

• "That looks difficult." ...

"Yes, we'll put that young Einstein chap on this job."

vs

• "Rimmer's struggling when it comes to avoiding asteroids. It's a good thing the deflector shields are working." ...

"Yes; do you think the skipper's put him in the right job?"

The first has 'job' = 'task', the second 'job' = 'post'.

From CED:

job [A2]

a particular piece of work:

• The builders are aiming to get the job done by the end of the month.
• [When I am working on a job I bear in mind that I am being paid for an assignment that an editor needs.][Linguee.com] .................

job [A1]

the regular work that a person does to earn money:

• When she left college, she got a job as an editor in a publishing company.
• It's very difficult trying to bring up two children while doing a full-time job.
• [Good employees don't want to work in a job where they're not trusted by leadership.] [kununu]