In Captain America, Schmidt states that the Tesseract was an Asgardian artifact, indeed one that belonged to Odin himself.
Tower Keeper: What you seek is just a legend.
Johann Schmidt: Then why make such an effort to conceal it? The Tesseract was the jewel of Odin's treasure room. Not something one buries. But I think it is close, yes?
How did he know this?
Johan Schmidt pushes the boundaries of science. Although supported by better scientific minds, he is very much on the fringe of what's possible with current (1940's) science.
The Tesseract has been hidden incredibly well. That castle is an old building that has clearly been guarded (and forgotten by others) for a long time.
The tower keeper himself seems distraught at the death of his family and loved ones, yet he does not kneel to Schmidt even after learning of their deaths. This means that he is devoted to his duty as a guardian, and considers hiding the Tesseract as his life's purpose. This further proves how diligently the Tesseract has been hidden.
Schmidt appearing in the castle already proves that he did his homework. This was not a trivial location to have a look for the Tesseract. It stands to reason that Schmidt would know everything about the Tesseract before knowing its hidden location. General knowledge about the Tesseract would be comparatively easier to find than the actual Tesseract.
Also look at the scene where Schmidt first activates the machine; and then very confidently pushes the machine over its safe limits, without any idea as to what will happen and a strong suggestion from the scientist (who built the machine) to not do so. Schmidt, while a scientist at heart, is driven by his belief that this machine will do what he wants it to do, and he completely foregoes any safety precautions or even measured expectations.
So the answer to your question can be distilled from the things I've mentioned.
Or, to condense this into a shorter answer: He had become an expert on Tesseract knowledge; because he needed to locate it at all costs.
Schmidt spent his time studying historical documents and artifacts in order to ascertain more information about where they came from, where they were and how to use them. In the Marvel universe, these artifacts are real as well as the origins. There are ruins and documents from Asgard as well as folk tales that tell of the mighty artifacts of the Asguardians. Thus it is simple to say that in his investigations he came across evidence of the Tesseract and where it came from.
As Thor and Odin and most Asgard was in norse mythology.
So, Tesseract was a real jewel in Odin's room (not an Infinity Stone). Marvel just bended it as a Infinity Stone.
So, Schmidt must have read it somewhere in that norse mythology.
