Is there a way we can get money for our research paper? Do research journals pay us for a research paper? Or can we sell the research paper?
Certainly Yes. There are two ways of earning money from publication:
Indirect as @seteropere explains by improving your visibility and getting higher chance of being recruited in higher quality institute with higher payment.
Direct: In many academic or even industrial institutes, researchers are being paid and are bound to perform research and publish paper in certain journals or conferences (mostly journal). If they fail, either they will be fired or will be punished. In order to avoid such experience, many are hiddenly searching for an opportunity to buy a paper in high price. Moreover, there are some universities that pay incentive to publish in journals (like US$ 2000) for each paper published. For instance, I know several people at such universities that need to improve their world ranking via publication and hence pay good money to publish in high-quality journals. But, selling or buying paper is considered unethical because we believe research is something we cannot buy. If we can buy research, it will not be research and will be a project.
can we earn money through a research publication?
Good publications make you a stronger candidate when apply to grants. It also help you in securing a job; if you do not have one. Also, collaborating with industry could be another way for earning money. Selling publication is something I never heard in my field (computer science). I do not even think it is possible in other fields.
If you are looking only for money then doing research is one of the bad choices you have.
In Germany, the "VG Wort" collects copyright fees put on copy machines, electronic library copies, etc., and redistributes these fees to authors.
Authors of research papers published in print can give note about their publications to the VG Wort and will then participate in the distribution of these fees. The calculation of what each author gets depends on the length of the articles and the number of authors, and in my experience one should expect a one-time payment of about 20 to 40 Euro per journal article.
If you register your idea as a patent, then everybody who wants to use your idea has to pay to you. However, universities (companies) usually claim the intellectual property of the patents, which means the inventor does not get that much incentive out of a patent. It is an exception if you work independent or self employed. Also, you can negotiate with university to have keep the intellectual property of your invention or discoveries.
According to this Scholarly Open Access blog entry, the Journal of CENTRUM Cathedra: The Business and Economics Research Journal pays US$2500 for each paper published and also pays US$500 for each peer review. It also seems that the Journal of Information Ethics used to pay US$50 per article published.
Certain types of papers can be supported by journals. These can include invited review articles, where the journal specifically seeks out the author to publish something on their field of expertise. The payments are usually minimal relative to the work required - on the order of US$300-500 - and are sometimes referred to as an "honorarium."
The key element here is that this money is paid because the journal specifically wants a paper from that author - presumably because they expect the work to be prestigious or highly cited.
This is by no means universal, but it has happened to me.