Periodic signals called Steady-State Visual Evoked Potentials (SSVEP) are elicited in the brain by flickering stimuli. They are usually detected by means of regression techniques that need relatively long trial lengths to provide feedback and/or sufficient number of calibration trials to be reliably estimated in the context of brain-computer interface (BCI). Thus, for BCI systems designed to operate with SSVEP signals, reliability is achieved at the expense of speed or extra recording time. Furthermore, regardless of the trial length, calibration free regression-based methods have been shown to suffer from significant performance drops when cognitive perturbations are present affecting the attention to the flickering stimuli. In this study we present a novel technique called Oscillatory Source Tensor Discriminant Analysis (OSTDA) that extracts oscillatory sources and classifies them using the newly developed tensor-based discriminant analysis with shrinkage. The proposed approach is robust for small sample size settings where only a few calibration trials are available. Besides, it works well with both low- and high-number-of-channel settings, using trials as short as one second. OSTDA performs similarly or significantly better than other three benchmarked state-of-the-art techniques under different experimental settings, including those with cognitive disturbances (i.e. four datasets with control, listening, speaking and thinking conditions). Overall, in this paper we show that OSTDA is the only pipeline among all the studied ones that can achieve optimal results in all analyzed conditions.