Shepherd, who joined City on a season-long loan last summer, had a clause inserted into his deal allowing him to potentially return to Oakwell in January.
Injuries to Reds defender Josh Earl and Marc Roberts last month potentially muddied the waters in regard to Shepherd staying at City, but it has now been agreed that he will continue his season-long loan in West Yorkshire.
Alexander has also confirmed that fellow defensive loanee Jay Benn, signed from Lincoln City at the end of the summer window, will also be staying put.
Alexander said: “Jay was with us until the end of the season anyway when he signed him. So there was no clause in there about him being recalled.
“With Jack, there was. We spoke to Barnsley prior to the (last) weekend actually to extend it to the end of the season because we have been delighted with how he has done.
“He’s been really happy with his exposure to first-team football and has really enjoyed his time with the boys and team.
“We spoke to Barnsley and tried to clarify that he was going to be with us for the rest of the season and we’re delighted to get that done.
“He played last Saturday and the game before and are delighted to keep him.”
Shepherd has featured times for City this term.
Meanwhile, the City chief is backing stricken striker Andy Cook to win his fitness battle after being ruled out for the rest of the season with a cruciate injury and believes that the discipline he has shown in the last 12 months regarding his physical conditioning will be a significant aid in his road back to full fitness.
Alexander commented: “When we gave him the news, he was devastated and obviously really upset. But he’s got slightly better and is getting his head around it.
“There will be peaks and troughs along the way and that’s me speaking as a very inexperienced person in those situations. But I have been around a lot of players who have had similar injuries and there’s a couple in our squad who he has already spoken to and they have given him encouraging words.
“He will have all the support he needs. When I spoke to him after I said: ‘Look, the discipline and way you have looked after yourself in the last 12 months is what you need to continue now.’
“Because he has looked after himself so well, he is in a much better position than he might have been with this injury and I think his healing time will be quicker and getting back to fitness when he gets out on that grass.”
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