Calderwood Developments asked for permission to develop a derelict former medical centre on Barnsley Road in South Kirkby earlier this year.
But local residents and councillors had safety concerns about where the proposed entrance to the supermarket's car park would be, and asked the applicants to consider moving it to another part of the site before making a final decision on the plans.
But Calderwood said that they had looked at alternative entrances but ruled them all out, and instead complained to the government about how quickly the council had handled the case.
An independent Planning Inspectorate will now decide whether or not the original plans, which would see the Co-op move in to the building as a tenant, can go ahead.
But now, documents attached to the planning application show that Calderwood has applied for Wakefield Council to foot the bill for its own appeal, claiming that the local authority has "behaved unreasonably".
The move was branded "despicable" by South Kirkby councillor Steve Tulley (Labour), who previously described the original proposal as the "worst planning application I've seen in 40 years", from a health and safety perspective.
Coun Tulley said: "I'm really quite surprised by this.
"It was obvious to everyone that the way the supermarket would have been built was inadequate, with the entrance where it was. I've lived here for more than 60 years and I've seen the increasing volume of traffic moving up and down.
"We were quite reasonable and asked the applicants to look at it again.
"For them to be trying to access public money for this, I find it disgraceful and despicable."
In its submissions, Calderwood says that Wakefield Council, "Has behaved unreasonably and that unreasonable behaviour has directly caused the appellant to incur unnecessary or wasted expense in the appeal process."
It goes on to claim, inaccurately, that the original proposals for the supermarket were refused planning permission. At a July meeting a decision on the matter was deferred to allow for further talks between the council and the applicants.
However, council officers later said that Calderwood decided not to attend meetings, and appeal to the government instead.
South Kirkby councillor Michelle Collins, who opposed the plans, said: "The applicants talk about wanting to be at the heart of the community, but this action shows they care more about profit than the local community.
"Instead of trying to talk to people about their concerns, the applicants have decided to take the matter to the government and are now trying to charge the very people of this community to get what they want anyway."
Calderwood were contacted for comment, but did not respond.
Wakefield Council said they were aware of the application for costs, which will soon be decided by the government along with the original plans.