I do believe you are confusing two different units. Yes there was a 37th Mississippi Infantry. Here is some info on it.
37th Regiment, Mississippi Infantry
37th Infantry Regiment was organized during the spring of 1862 with men recruited in the counties of Clarke, Lowndes, Greene, De Soto, Jasper, and Claiborne. After participating in numerous battles in Mississippi the unit was assigned to General Hebert's Brigade in the Department of Mississippi and East Louisiana. It was captured when Vicksburg fell and during the siege it lost 17 killed, 56 wounded, and 7 missing. Exchanged, the regiment contained 26 officers and 442 men in December, 1863. It then served under Generals Mackall, Cantey, and Featherston in the Army of Tennessee. The 37th fought in the Atlanta Campaign, endured Hood's winter operations in Tennessee, and ended the war in North Carolina. It reported 5 killed and 27 wounded of the 453 engaged at Iuka , had 19 killed and 62 wounded at Corinth, and sustained 81 casualties at Hatchie's Bridge. Many were disabled in Tennessee, and early in 1865 its ten companies were reduced to three and the unit was redesignated the 37th Battalion. It surrendered in April. The field officers were Colonels Orlando S. Holland and Robert McLain; Lieutenant Colonels William S. Patton, Samuel H. Terral, and William W. Wier; and Major John McGee
There was also a 34th Regiment, called the 37th,
34th Regiment, Mississippi Infantry
34th Infantry Regiment [also called 37th Regiment] was organized at Holly Springs, Mississippi, in April, 1862. The men were drawn from the counties of Tate, Smith, Marshall, Tippah, Holmes, and Benton. Serving in General Walthall's and Brantly's Brigade, the unit fought with the Army of Tennessee from Chickamauga to Atlanta, then saw action in Tennessee and North Carolina, It lost 15 killed, 91 wounded, and 19 missing of the 307 engaged at Chickamauga, and reported 235 casualteis at Chattanooga. In December, 1863, it was consolidated with the 29th and 30th Regiments and totalled 554 men and 339 arms. The 34th had 15 disabled in the fight at Resaca and 18 at Ezra Church. It surrendered on April 26, 1865. The field officers were Colonel Samuel Benton; Lieutenant Colonel Daniel B. Wright; and Majors Thomas A. Falconer, Armistead T. Mason, and William G. Pegram.
I checked the name of your ancestor, and Evans D. Reaves was in Co. E, 37th Mississippi, the first unit I mentioned here. The only change of designation for this unit was when it was so depleted by service that it was designated as a battalion rather than a regiment. Thus the 37th Mississippi Battalion. You could not find your ancestor in the 34th because he was not there. All his references would be in the 37th Mississippi Infantry Regiment or 37th Mississippi Infantry Battalion.
I hope this helps.
I know that Civil War unit designations can be confusing. Especially confederate units.