Statistical pattern recognition has been considered to be one of the most successful approaches in the recent advancement of speech and speaker recognition. Out of all the approaches Hidden Markov Models, Gaussian mixture models and Vector Quantization has been considered to be one of the most successful techniques in regards to the performance of the speaker recognition systems. However the performance of these techniques degrades when subjected to limited data condition and noisy environment. Fuzzy approaches with their variable fuzzy parameters may reduce the degradation. This paper attempts to highlight the effect of learning parameter of objective function while implementing Fuzzy Vector Quantization on Text Dependent Speaker Verification under limited data condition and also under practical noisy environment. The entire set of experiments were performed between learning parameter m=1.1 to m=2 and the system accuracy was observed in each case. The experimental results performed on telephonic database suggests better results for learning parameter m=1.37 where the maximum accuracy of the system reaches 84.81%. However the performance of the system also depends on codebook size. Our research focuses the effectiveness of the variation of learning parameter in speaker verification performance and robustness of the system.