Do you understand the time and costs involved in filing a patent? 10 years ago it was $30-35K and 4 to 5 years to issue. Doubt it's gotten better.
This has improved drastically since the USPTO now offers the 'file as a micro entity' deal for those with low income, have less than 5 existing patents and are filing privately. Again, repeat from my above post: google 'USPTO micro-entity patent rules'. The program came about in 2013, so it's new. I already received my letter of acceptance for a patent issued 6 months ago staying within the rules and it will be accepted in the new year.
Also, most patents are pretty easy to work around - thus reducing the value of a single patent. And, you will need to spend time and money to defend your patent - bring money, guns and lawyers.
Yes, this takes a hell of a lot of money. You are not prepared to go down this route if you are seeking mere employment. The only use for your patent here is either to sell/license, or, if you have access, to get investment with those who have the deep pockets and legal backbone who will support you.
You need to be absolutely certain that you have a world class idea and write a patent that locks down any possible workarounds.
Yes, the vast majority of patents do nothing, make no money and just site there. It's takes more than just having a good unique idea to succeed here.
To cover the workarounds, unlike my earlier patents, which I sold (it's what paying for the new one...), my current one is over 120 pages long. It is that good of an idea, and I wanted to cover all the work arounds. Even though my filing fees were cheap because of the new 'micro-entity' filing feature, I had professional help with the text and claims, so, it still came to 30k$, and now, before the US does the final grant, I'm spending another 15K for a PCT filing which gives me a 2.5 year window to file in other countries which costs even more, I'm looking at around an additional 100K$ to get the countries I want. Be aware I have experience with my 3 prior patents and have an avenue for either investment or sale of this patent.
Like I said earlier, use google. You can search US patents there, they are complete and you can also search on the USPTO website. As I said, do your due diligence. Completely read other patents in the same field as your invention. Verify who wrote them, who owns them. Do you understand when I say in my previous post that you make a set of claims in your patent & you can have multiple claims, some in independent form. Even my latest patent took me 6 months to write and gone over with my patent agent making sure every single word, position of each sentence, figures and illustrations, and in the claims section, every comma, semicolon, hyphen and indentation COUNTS.......... + I've done searches of existing patents to check for prior art and list citations in my current patent to cover every angle possible and make sure no one can work around my core idea, and be sure, they cant. But to achieve this, I was doing nothing but editing text, testing, and illustrations for 6 months to make my first really big $$$ patent.
(This one is in a class way above my older 3 from 15 years ago, if you haven't figured it out, the 2 google search examples I posted would show you 2 of mine which I sold.)
If it is in the scope of the job offer, then you need to discuss it with the company up-front. My guess is your great offer came about because of your expertise in that area. It's murky - as other have said, talk to an attorney.
This can get ugly.... No matter what, keep your idea a secret. You may only tell your full idea under trust to an attorney you are seeking help from if he requires that much specific information from you.