There actually is, or perhaps better said was, such a word in the adverb othertimes. However, the OED says that othertimes is now obsolete. It was not uncommon in Early Modern English up through the 18th century, but its use declined during the first half of 19th century. It tends to oppose sometimes.
Democritus would sometimes say that the images and their circuitions were Gods, and othertimes this Nature, which disperseth these images, and then our knowledge and intelligence. (Essays of Michael Lord of Montaigne)
The first appearances were, a low state of health, depressed, exhausted, and sallow look — the eyes sunken, sometimes of glossy whiteness, othertimes icteric, with dark areolae around — nose pinched — mouth blanched — except where ... (Researches on Primary Pathology: And the Origin and Laws of Epidemics)
As often as the Devil appeared to the Mexicans, they made immediately an idol of the figure in which they bad seen him ; sometimes as a lion, othertimes as a dog, othertimes as a serpent ; and as the ambitious Devil took advantage of this ... (The Poetical Works of Robert Southey)
This adverb eventually came to be used as a noun serving as a prepositional object for in and at, and finally people gave up and wrote a space between the two words:
- at other times
- in other times
Which is where we stand today. People may well ask “why” something did or did not happen in language, but most such questions have no possible concrete answer.
The historical record shows many combinations with any, other, some, when, time, times that are now rarely seen. Combining the old ones with the extant ones, and disregarding hyphens, the list of such adverbs is very long:
aforetime, anyplace, anyway, anyways, anywhen, anywhence, anywhere,
anywhither, anywise, beforetime, betimes, daytimes, elsehow, elsewards,
elsewhat, elsewhen, elsewhence, elsewhere, elsewhither, elsewho, elsewise,
everywhen, foretime, heretoforetime, midtime, mostwhen, noontimes, nowhen,
oftentime, oftentimes, otherlike, otherliker, othertime, othertimes,
otherward, otherwards, otherways, otherwhat, otherwhence, otherwhere,
otherwheres, otherwhile, otherwhiles, otherwhither, otherwise, overtime,
sometime, sometimes, someway, someways, somewhat, somewhatly, somewhen,
somewhence, somewhere, somewhile, somewhiles, somewhither, somewho,
somewhy, somewise, toforetime.