There are currently two questions with answers mentioning paraconsistency, https://math.stackexchange.com/search?q=paraconsistency, which would suggest that there is really no need for the tag. This figure, however, seems a bit misleading since, on the other hand, there are 63 results mentioning "paraconsistent". https://math.stackexchange.com/search?q=paraconsistent. After a brief glance, most of these questions deal with technical issues, some of them within logic, some within computer science (which, in the context of artificial intelligence, is one of the main areas where paraconsistency is investigated). This suggests there is a demand, although admittedly small, for the tag.
It seems to me that the kind of already existing questions that could use the tag suggests that there is a market, albeit small, for it. Combining this with the mere number of questions mentioning the keywords above which, although not terribly large, is not insignificant, I can see some of the benefits of having the tag around. By way of contrast, there are 37 questions with the tag combinatory-logic, 16 with the tag second-order-logic, 13 with the tag categorical-logic, and only 3 with the tag relevant-logic. I confess the latter I found quite surprising, I would have expected a significantly larger number.
None of the current logic-related tags suggest or hint at the specific topics one may want to discuss in the context of paraconsistency, so I don't feel the tag would be redundant. I also don't feel it would be useless, as I expect that there are questions that could use the tag and are simply "invisible" at the moment to their intended aaudience. Let me give a closely related example to illustrate this last claim. There are several questions on the site pertaining to knowledge bases, and they are tagged logic, sometimes combined with something else, because we do not have a tag for knowledge bases or many of the other topics that appear in the setting of logic in computer science. Even some experts in logic may be unaware of what knowledge bases are, so the current tags are not terribly useful here. A more specific tag would very likely help. I believe paraconsistency would benefit in a similar way.
An objection to having this tag seems to be that people who are not aware of the meaning of the word would not benefit from it. That said, as mentioned in the comments beneath the question, people who use the site may actually learn about it by reading questions carrying the tag. In that sense, I do not find the tag useless or superfluous. (I admit I do not know statistics indicating that this has been a side benefit of introducing other tags.)
I would be happy to create the tag if it comes to that, so that Teg or other users who may be interested in having it around do not have to wait until they reach the 1K reputation requirement to create it themselves.