Often, you can get free legal advice, here. NVLSP is a nationwide program (non profit) that helps Veterans with legal needs. Things like Nehmer Vets, (normally Vietnam Veterans), discharge upgrades, and Veterans appeals to the CAVC are some of the things they often do. You need a DD214, they screen out "fake" wannabe Veterans.
https://www.nvlsp.org/what-we-do/lawyers-serving-warriors
Importantly, also, IF YOU HAVE A RECENT BVA DENIAL (120 days) you can usually take your pick of a NOVA attorney to represent you at the CAVC and EAJA pays the fees. Be sure and discuss this with your potential attorney, their fee plans vary. Since EAJA pays the fees, its no cost to you.
Many attorneys, if they think your BVA denial is wrong, will accept payment EXCLUSIVELY from EAJA, you pay nothing.
Pick from one of these attorneys most of which specialize in helping Veterans:
https://www.vetadvocates.org/directory/widget_search?current_page=1&sort_type=featured&filter={"additional_info.show-profile-on-sustaining-membership-directory"%3A+"yes"}&asset_type=company_user&display_type=default
Source: Personal experience. I have hired a lawyer several times and paid little or no fees.