I am a resident of Ballia district of Uttar Pradesh . I have read somewhere that it has been named after Raja Bali the demon king who was sent to Hell by Vaman avatar of Lord Vishnu. It is said that the original name was Baliyag "the place where Bali performed yagna" just like Prayag which was named after Prajapati doing yagna. Later the name was deprecated and changed from Baliyag to Baliya/Ballia . Is it true or just a rumour? https://www.quora.com/Who-what-is-Ballia-Uttar-Pradesh-named-after#
Chapter 18 of Canto 8 of Srimad Bhagavatam Verses 20 to 22 describes the Yagyashala of Bali chakravarty whither Lord Vamana went. This English transcript is from Srimad Bhagavatam of Srila Bhaktivedanta Prabhupada - the founder of ISKCON:
"(20) As soon as He heard about the glory of Bali as someone who under the guidance of Bhrigu brahmins performs horse sacrifices, He headed for the location where they took place and with each step that He as the Complete and Fully Endowed Essence made on His way, He therewith imprinted the earth with His footsteps. (21) At the northern bank of the Narmadâ river in the field of Bhrigukaccha where all the priests of Bhrigu were performing their rituals for the sake of the ultimate ceremony [the horse sacrifice], they saw Him in their presence [radiating] like the risen sun. (22) The priests as also Bali, the instigator of the yajña and all who had assembled there, were overshadowed by Lord Vâmana's splendor, oh King and wondered whether they saw the sun rising, the god of fire or Sanat-kumâra who wanted to attend their ceremony."
Ballia is a city with a municipal board in the Indian state of Uttar Pradesh bordering Bihar. The eastern boundary of the city lies at the junction of two major rivers, the Ganges and the Ghaghara. To the best of my knowledge Narmada flows nowhere near Balliya nor is it situated on the Northern Bank of Narmada.
The claim, therefore, is spurious and a rumour.