Saviour of all people, ESPECIALLY of those who believe 1 Timothy 4:10 reads:


  That is why we labor and strive, because we have put our hope in the living God, who is the Savior of all people, and especially of those who believe. [NIV]


Is there any historical use of this text by known early adherents to Universalism?

(See also this parallel question about the origins of this verse.)
At least three early adherents of apocatastasis refer to this passage.  But not all their references to it are necessarily defenses of that particular doctrine.  For example, Origen uses it to argue for the general love of God for his creation:


  We both read and know that God loves all existing things, and loathes nothing which He has made, for He would not have created anything in hatred. [...] For He Himself is said to be the Saviour of all men, especially of them that believe; and His Christ to be the propitiation for our sins, and not for ours only, but also for the sins of the whole world. (Against Celsus, 4.28)


Clement of Alexandria's Stromata is often cited to demonstrate his belief in universalism, and he quotes this verse in it:


  And to speak comprehensively, all benefit appertaining to life, in its highest reason, proceeding from the Sovereign God, the Father who is over all, is consummated by the Son, who also on this account “is the Saviour of all men,” says the apostle, “but especially of those who believe.” (6.17)


He also quotes it in Exhortation to the Heathen, which may be the earliest reference to the verse by a universalist (c. 195):


  You may, if you choose, purchase salvation, though of inestimable value, with your own resources, love and living faith, which will be reckoned a suitable price. This recompense God cheerfully accepts; “for we trust in the living God, who is the Saviour of all men, especially of those who believe.” (Chapter 9)


And finally, Gregory of Nyssa cites the verse in his argument for the trinity, "On 'Not Three Gods'":


  And as the Saviour of all men, specially of them that believe, is spoken of by the Apostle as one, and no one from this phrase argues either that the Son does not save them who believe, or that salvation is given to those who receive it without the intervention of the Spirit; but God who is over all, is the Saviour of all, while the Son works salvation by means of the grace of the Spirit, and yet they are not on this account called in Scripture three Saviours


There's some debate over whether these three all believe in "universalism" as it is defined today.  But these three authors are certainly among the most likely candidates for that label in the early church.