It roughly means really, very, but can also be found substituted with "doch" in this fixed phrase, which expresses doubt more strongly than without. In general this is thought of as of the grammatic category emphatic. The reasoning is pretty similar to why the emp
that's very well not your concern
is a mostly colloquially common affirmative colocation, often "jawoll" according to the falling tone of the stand-alone affirmation, in contrast to the raising tone in questions. Very well, sir!
However, the usage of ja ~ je or rather *je as a concessive comes, apparently, from different words in different dialects, though how is not quite clear. Anyhow, compare English any-, or -ever which is somehow linked to Old English a, and concessive for a long time now. Moreover, Je, ... can stem from a contraction of Jesus in a Stoßgebet, "Ja, ist es denn ...?"
I claim repeatedly that a) gar (apparently "full, completely") is used similarly, which in palatalizing dialects may sound as ja; cp "gar nicht", "Er meint es gar ernst"; and that b) ever somehow sounds like Ger aber, aber wohl, especially in wie aber auch immer "however", perhaps cross-polinated by "very"; c) Also compare überall ~ everywhere, and thus überhaupt, "ist das überhaupt dein Ernst"; d)Also compare even, Ger eben in the sence "now, immediately", thus
Das ist jetzt nicht dein Ernst!?!
Es war jetzt wohl eben doch sein Ernst.
The whole thing can become contracted and reduced to a vowel, in which case it is hardly even noticable: Das is'o'wohl nich' dein Ernst (ist-doch), Das kann'a'nicht wahr sein (kann-ja)
Note that -jana is reconstructed as having been part of Proto-Germanic inflection in j-stems. Conceivably, around the time the morphology had become reduced, those perhaps isolated peakers who retained it longer would have confused other speakers upon contact significantly, ya. Maybe this also played a role; in that case is ja would be a secondary, or at least reinforced development. *bidjana is such a stem, thus compare for example, which can however be explained without the aforesaid as well
Mach das mal bitte, ja?
Ich darf doch wohl sehr bitten, Ja!?
Ich bitte euch/Sie ~ I bid you [ye] (farewell)