Was there ever any issue with any type of vaccine that did not occur within weeks of administration? I remember reading an article that said that serious advers

Was there ever any issue with any type of vaccine that did not occur within weeks of administration? I remember reading an article that said that serious adverse effects of vaccines either occur soon after giving them or not at all. That does not mean that there could not be any or that we should not look but that from what we seem to know about how vaccines work, it would be very unlikely to find anything like that.