The tweets from an account in the name of Barker were sent to Arter after Arsenal came from 3-0 down to draw 3-3 at Bournemouth on Tuesday night. One of the messages said: “at least you didn’t lose your kid”.
It was then followed up by another tweet to the Ireland international which said: “big hype just for a disappointment like the 9 months leading up to your childs birth”.
Yesterday, Barker issued an apology for what he described as “disgraceful comments” and later the account was deleted.
Southern Football League Premier Division side Hitchin hold Barker’s registration.
The 19-year-old forward has, though, this season been mainly playing in the Spartan South Midlands League Division One, first on loan at Langford, where he made five appearances, and then more recently Codicote.
Hitchin issued a statement yesterday afternoon announcing they were “terminating Alfie Barker’s registration and relationship with the club with immediate effect”.
The FA say it will seek Barker’s observations in relation to the postings from his social media account.
Bournemouth and Arter became aware of the posts following the match and reported them directly to Twitter, who have stated the organisation does not comment on individual accounts for privacy and security reasons.
A Dorset police spokesman said it had not received any complaint about the social media postings and was therefore not investigating them.
Yesterday morning, the tweets were still available for public view on the social media site. However, the offensive posts were later deleted as Barker issued an apology.
He wrote: “Im sorry for every comment made , id like to apologise to harry arter and his family , for such disgraceful comments and im sorry...”
A second message then added: “.. from the bottom of my heart.”
Barker replaced his Twitter profile picture with just a black screen and altered his bio to first read “Got Hacked” then simply a single full stop.
By yesterday afternoon, the Twitter account was no longer in use.
Hitchin confirmed they had decided to sever all ties with the player.
“The club adopts a responsible approach to social media and would expect any player connected to Hitchin Town to do likewise,” the club statement read.
“We would reiterate that Hitchin Town, as a community club with established links with various segments of the public, has been a long-time user of social media channels and expects all club stakeholders to use them appropriately.”
Langford confirmed Barker had left the Spartan South Midlands League Division One club “in September last year to follow his playing career”.
Barker went on to join up with Codicote, where he scored 20 goals in 17 appearances.
However, following the developments of Tuesday night and yesterday morning, Codicote also issued a statement saying the club had “no choice but to terminate our relationship with him”.
Barker’s Codicote strike partner Marc Arnott said: “I don’t know if the tweet was meant to be funny and looking for a thousand retweets.
“I’ve got a 10-week old baby. One of my mates has lost a baby.
“No-one (who hasn’t experienced it) knows the pain of losing a child.”
Barker was in the process of being transferred to Spartan South Midlands League Premier Division side Stotfold.
However, Stotfold chairman Phil Pateman said in a statement to Press Association Sport the club had now “withdrawn our interest in the player, with immediate effect”.
Arter has a tattoo on the inside of his right forearm which is dedicated to his daughter Renee, who was stillborn in 2015.
The 27-year-old’s fiancee Rachel is currently pregnant and due to give birth to a baby girl in February.