Combat employment
BA-3 and BA-6 armored cars were supplied to arm reconnaissance troops of tank, cavalry and infantry units of the Red Army. In 1937, a motorised armored regiment was formed in the Transbaikal Military District, which, shortly afterwards, was expanded into a brigade.
It included a battalion of medium armored cars, a reconnaissance battalion (medium and light armored cars) and an infantry machine gunners' battalion. In total there were 80 medium and 30 light armored cars in the brigade. Three such brigades — 7th, 8th, and 9th participated in fighting with the Japanese army at the Khalhin-Gol River.
Virtually at the same time as the armored cars were being supplied to the Red Army, they were also exported to other countries. Foreign sources tell us about the sale of 60 BA-6 armored cars to Turkey.
However, if the date of the sale is correct, then the vehicles were most likely BA-3's, since the production of the BA-6 did not begin until one year later. This assumption seems valid from an operational point of view as well. It would be easier for the Turks to perform service on the American Ford Timken chassis rather than on the Soviet GAZ-AAA. However, this is my guessing only...
Starting in December 1936 and lasting up until the withdrawal of Soviet military assistance in 1938 Spain took delivery of 7 BA-I's and 80 BA-6's. One of the first units of the Republican army that received the machines was the 1st Armored Brigade under the command of D. G. Pavlov. This brigade took part in the heavy battles near Madrid in 1937. The crews of the tanks and armored cars were made up of Soviet and Spanish soldiers. During fighting near Madrid, the BA-6's took out several enemy tanks.
By the summer of 1937, an armored car brigade was formed in the Spanish Republican army. In December 1937 up to 30 BA-6's with Spanish crews participated in an advance on the Teruels prominence — the last major and successful Republican operation. After the end of the Civil War, several BA-6's remained in the Spanish army until the early '50s.
BA-6's also served in the Mongolian Revolutionary People's Army. The 6th and 8th armored battalions of the Mongolian cavalry divisions equipped with these vehicles took part in an armed conflict at the Khalhin-Gol River during the spring and summer of 1939.
The foreign press cites instances of BA-6 deliveries to Afghanistan and China. It is hard to verify this information with respect to Afghanistan. As to China, such deliveries seem unlikely, because in the information released by the Soviet press concerning the delivery of military equipment and armaments to China between 1936 and 1939, the BA-6 armored cars (or any other armored cars) are not mentioned.
Thus, 150 BA-I, BA-3, and BA-6 armored cars were exported between 1935 and 1939. Most of the others performed service in the Red Army, primarily on the Far East. Nevertheless, a few BA-3's and BA-6's took part in a Polish campaign (1939), during the Winter War, as well as in the Great Patriotic War (they could be found in the military forces at least as late as the middle of 1942).
The Finish army, which captured some of these vehicles in 1939 and 1941, exploited them much longer. As of June 1, 1944, the Finns had possession of one BA-3 (which served until the end of 1944) and 10 BA-6's (which were in operation until the end of 1956.) Currently an example of a BA-3 armored car (#5633) is kept in the tank museum in Kubinka; and a BA-6 (#4382) can be seen on display at the 
CMVS in Moscow (see photos below the article).
In conclusion it should be noted that at the time of creation and even in the first stages of WW2, these armored cars were the most heavily armed in the world. Their British and American counterparts acquired 37–40 mm guns only in 1942. The first adequately armed German armored car became the widely known «Puma» (1944).
Unfortunately, massive armament was perhaps the only and most important merit of the medium Soviet armored cars of the '30s. Battle experience revealed the practical impossibility of their deployment on the front lines due to poor off-road capability.
The list of major shortcomings included weak armor and a lack of a driving controls post in the rear. The most advanced representative of the large series of Soviet gunned armored cars — the BA-10, also exhibited these shortcomings. Incidentally, all foreign armored cars of those years built on the chassis of commercial vehicles suffered from the same «illnesses.» With the arrival of all-wheel drive wheeled armored cars they became completely obsolete.
