Here is a list of publishers that specialize in short stories in regional and local dialects:
Akashic Books - publishes fiction that features the diverse dialects and languages of urban communities.
Arte Público Press - publishes fiction in Spanish and English, focusing on the experiences of Mexican Americans and other Latino communities.
Biblioasis - publishes fiction and poetry from around the world, with a focus on regional and local dialects.
BOA Editions - publishes poetry and fiction that features the diverse voices and dialects of communities.
Cassava Republic Press - publishes fiction and poetry from Africa, with a focus on regional and local dialects.
Cinco Puntos Press - publishes fiction and poetry that features the diverse voices and dialects of Latino communities.
Curbside Splendor - publishes fiction and poetry that features the diverse voices and dialects of communities.
Graywolf Press - publishes poetry and fiction that features the diverse voices and dialects of communities.
New Directions - publishes fiction and poetry from around the world, with a focus on regional and local dialects.
The New Press - publishes fiction and nonfiction that features the diverse voices and dialects of communities.
Please note that this list is not exhaustive and there are many other publishers that specialize in short stories in regional and local dialects. Additionally, many mainstream publishers also have imprints or lines dedicated to publishing works in regional and local dialects.