Acid or hydrogen phosphites are called hydrogenphosphonates or acid phosphites.  IUPAC recommends the name hydrogenphosphonates).  They are anions HP(O)OH.  Aypical derivative is the salt [NH][HP(O)OH]. Many related salts are known, e.g., RbHPHO, CsHPHO, TlHPHO.  These salts are prepared by treating phosphorous acid with the metal carbonate. These compounds contain a layer polymeric anion consisting of HPO tetrahedra linked by hydrogen bonds. These layers are interleaved by layers of metal cations.
Organic esters of hydrogen phosphites are anions with the formula HP(O)OR (R = organic group).  One commercial example is the fungicide fosetyl-Al with the formula [CHOP(H)O]Al.