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Automatic emotion recognition plays a significant role in the process of human computer interaction and the design of Internet of Things (IOT) technologies. Yet, a common problem in emotion recognition systems lies in the scarcity of reliable labels. By modeling pairwise differences between samples of interest, a Siamese network can help to mitigate this challenge since it requires fewer samples than traditional deep learning methods. In this paper, we propose a distance loss, which can be applied on the Siamese network fine-tuning, by optimizing the model based on the relevant distance between same and difference class pairs. Our system use samples from the source data to pre-train the weights of proposed Siamese neural network, which are fine-tuned based on the target data. We present an emotion recognition task that uses speech, since it is one of the most ubiquitous and frequently used bio-behavioral signals. Our target data comes from the RAVDESS dataset, while the CREMA-D and eNTERFACE'05 are used as source data, respectively. Our results indicate that the proposed distance loss is able to greatly benefit the fine-tuning process of Siamese network. Also, the selection of source data has more effect on the Siamese network performance compared to the number of frozen layers. These suggest the great potential of applying the Siamese network and modelling pairwise differences in the field of transfer learning for automatic emotion recognition.