The city’s Licensing Board is now hearing applications for the remaining 25 affordable liquor licenses, the last batch approved by the legislature and the best hope for a number of small restaurants who cannot swing the sky-high cost of full licenses on the open market.

On top of the existing city cap, the legislature in 2014 allocated an additional 75 licenses for distribution over three years, this marking the final group. In each group of 25 licenses, five are all-alcohol and can be awarded to establishments across the city.

The remaining 20 — five beer and wine, 15 all-alcohol — are neighborhood restricted. Their issuance is limited to historically underserved neighborhoods including Roxbury, Dorchester and Jamaica Plain.

These annually renewed, neighborhood-specific licenses cannot be sold or transferred by the licensee once acquired. They come at a reduced price, topping out at around $3,000 for an all-alcoholic license. Restaurateurs seeking permits on the open market could expect to shell out $50,000 for a beer and wine license or up to $450,000 for an all-alcohol license.

City Councillor Ayanna Pressley, who has championed the neighborhood licenses as a way to enliven communities in need of local restaurants, pointed out in August that Boston’s lack of local control over the distribution of the licenses means applications are considered on a first-come-first-serve basis.

All licenses are still available, a spokeswoman for the licensing board said Tuesday.

The licensing board hears applications for licenses each Wednesday, which may be voted on at Thursday sessions. Given the nature of the affordable licenses, the board is likely to consider them in large batches, rather than on a weekly basis.

At least three Dorchester petitions are presently up for consideration -- the Wahlburgers in South Bay Town Center and a Taqueria in Lower Mills are seeking neighborhood-specific all-alcohol licenses, and Molinari’s in Adams Village is applying for a beer and wine license.