Was a scroll with INRI inscription displayed near Jesus all the way to Calvary?

We read in Jn 19:19-20( KJV): > And Pilate wrote a title, and put it on the cross. And the writing was Jesus Of Nazareth The King Of The Jews.This title then read many of the Jews: for the place where Jesus was crucified was nigh to the city: and it was written in Hebrew, and Greek, and Latin. So, we have the INRI sign on every crucifix. Now, the images of the Stations of Cross in the Church of Blessed Sacrament in Washington DC depicts a soldier carrying a scroll with INRI written on it. In one station, Jesus himself is holding the scroll ( You can see them during the Exposition of the Blessed Sacrament and Divine Mercy Chaplet held in the Church and recorded in 2020, on YouTube). My question is : Was a scroll with INRI inscription displayed near Jesus all the way to Calvary ? Are there any extrabiblical writings available on the topic ?