The answer to that question is "....maybe?" It may depend on how much stock you place in legends. For the Ostrogoths--more specifically, for the reign of Theoderic and just before, we have a number of historical sources--chiefly Procopius, the anonymous Valesianus--who both wrote histories (Procopius being more from the Eastern Roman perspective)--and Cassiodorus, who served in Theoderic's administration and whose correspondence on his behalf is a fabulous resource. Cassiodorus also apparently wrote a huge work on the history of the Goths, which is now lost. But at this point the Ostrogoths are relatively settled. We do, however, have two longer accounts of the history of the Goths, and one of them, the Getica of Jordanes (a sixth century historian of Gothic ancestry), which is thought to be a summary of Cassiodorus' lost work, has a really interesting passage regarding very early Gothic women:

" (49) After his death, while the army under his successors was engaged in an expedition in other parts, a neighboring tribe attempted to carry off women of the Goths as booty. But they made a brave resistance, as they had been taught to do by their husbands, and routed in disgrace the enemy who had come upon them. When they had won this victory, they were inspired with greater daring. Mutually encouraging each other, they took up arms and chose two of the bolder, Lampeto and Marpesia, to act as their leaders. (50) While they were in command, they cast lots both for the defense of their own country and the devastation of other lands. So Lampeto remained to guard their native land and Marpesia took a company of women and led this novel army into Asia. After conquering various tribes in war and making others their allies by treaties, she came to the Caucasus. " (English translation source is here: https://people.ucalgary.ca/~vandersp/Courses/texts/jordgeti.html )
Note that this is from the semi-legendary past of the Goths many, many years before they migrate into Eastern Europe from what Jordanes believes is Scandinavia/ "Scanzia" (or Thule) These women (who go on to be described as "Scythian" as well), essentially turn into the Amazons. So what this tells us is that there was apparently a legend that Gothic women fought, and that Jordanes/Cassiodorus interpreted this as being the origins of the Amazons. But in the later works (Procopius and Anon. Valesianus) there are no mentions of Ostrogothic women fighting--although Procopius does mention that the women did accompany the army on the larger migratory campaigns--in the wagons with the children and "other chattels." (Procopius' history of the Gothic Wars in English translation is here https://www.gutenberg.org/files/20298/20298-h/20298-h.htm )

So to conclude: There is a legend about Gothic fighting women mentioned by Jordanes/Cassiodorus, but there is no mention that I am aware of in the primary literature that mentions Ostrogothic fighting women during the about 100 years where we hear about them most (from the period of their alliance with the Huns through to the reconquest of Italy under Justinian).