Schirmer is really not that prominent as publisher of string music. But I scanned at the catalog, since they publish so little, I find that whatever they publish, those items are often the very core of the repertoire.
Criteria: exclude studies, duets, and clearly works intended for students. Brackets is for birth year
Violin
Vitali (1632): Ciaccona
Corelli (1653): sonatas op.5
Vivaldi (1678): 4 seasons
Telemann (1681): sonatas
Bach (1685): Concertos in A minor, E major, G minor (BWV 1056R - reconstructed); Solos; Double concertos
Handel (1685): 6 sonatas
Leclaire (1697): Sonata #3 in D major
Nardini (1722): concerto in E minor
Viotti (1755): Concerto #2223
Mozart (1756): sonatas; concertos #3-5
Rode (1774): 24 caparices
Beethoven (1770): 2 Romances; sonatas; concerto op.61
Paganini (1782): caprices op.1; moto perpetuo op.11; concerto #1 in D
Schubert (1797): sonatinas op.137
Beriot (1802): Concerto #9; Scene de Ballet op.100
Mendelssohn (1809): concerto op.64
Schumann (1810): 3 Romances op.84; Fantasy pieces op.73
Franck (1822): Sonata in A major
Lalo (1823): Symphonie Espagnole op.21
Brahms (1833): Concerto; 3 sonatas
Accolay (1833): Concerto #1
Wieniawski (1835): Concerto #2 op.22; Polonaise Brillante op.4
Saint-saens (1835): Concerto #3 op.61; Havanise op.83; Introduction and rondo capriccioso op.28
Bruch (1838): Concerto op.26; Scottish phantasy op.46
Mussorgsky (1839): pieces
Tchaikovsky (1840): Concerto op.35
Dvorak (1841): Romance op.11, Sonata op.100; pieces
Sarasate (1844): Zigeunerweisen op.20
Sitt (1850): Concertino in E minor op.31
Viola
Telemann: Concerto in G
Beethoven: Notturno (op. 8/42)
Schubert: Arpeggione sonata
Cello
A. Scarlatti (1660): 3 sonatas
Vivaldi: 6 sonatas
Bach: Suites
Marcello (1686): 6 sonatas
Boccherini (1743): 6 sonatas
Chopin (1810): Sonata op.65
Lalo: concerto in D minor
Brahms: sonata #1