This could be him:
John Hermes, Company I, 68th Enrolled Missouri Militia, filed for Invalid Class pension, Application No. 12592 from Missouri, April 11, 1903
John Hermes, Company I, Enrolled Missouri Militia, filed for Invalid Class pension, Application No. 1298912, April 11, 1903
It appears that pension was not granted
Source Information
National Archives and Records Administration. U.S., Civil War Pension Index: General Index to Pension Files, 1861-1934 [database on-line]. Provo, UT, USA: Ancestry.com Operations Inc, 2000.
Original data: General Index to Pension Files, 1861-1934. Washington, D.C.: National Archives and Records Administration. T288, 546 rolls.
Company I - Captain Jasper Belken - Many men from Fredericktown, Madison County
See also:
https://www.google.com/search?site=&source=hp&q=68th+enrolled+missouri+militia&oq=68th+Missouri+&gs_l=hp.1.1.0i22i30l2.1645.8683.0.12938.15.14.0.1.1.0.269.1741.0j13j1.14.0....0...1c.1.64.hp..1.14.1473.0.PRFGJEya1vg