Source (image has been modified to indicate location of fins).
Well, those fins were put there to increase yaw and pitch stability on the D version because of the change in the centre of gravity due to a higher fuselage from the C version. This D model also had more powerful engines than the C model. To add on, the strakes at the bottom were added for the same reason too.
More info can be found here.
Some of the answers are referring to the dual aft strakes on the underside of the fuselage below the tail. The dual aft strakes are Indeed there to increase stability, specifically for one engine operations. They remove the yaw damper limitation. To answer the question, the 1900 has the same horizontal stabilizer as a King Air 200. Obviously the 1900 is far longer and bigger than the King Air 200 and needs those extra modifications on the tail. Basically it saved Beechcraft from redesigning an entire new tail, saving quite alot in design costs. Both the C and D models have the “fins” you have circled in your picture. If you think that the dual aft strikes are a bad design, you are completely wrong. Operators actually pay huge amounts of money to fit them to older model King Air 200s part of the Raisbeck upgrade. They improve efficiency and as mentioned earlier remove any yaw dampener limitation.