In this paper, we propose a novel approach to examine the risk spillovers between FinTech firms and traditional financial institutions, during a time of fast technological advances. Based on the stock returns of U.S. financial and FinTech institutions, we estimate pairwise risk spillovers by using the Granger causality test across quantiles. We consider the whole distribution: the left tail (bearish case), the right tail (bullish case) and the center of the distribution and construct three types of spillover networks (downside-to-downside, upside-to-upside, and center-to-center) and obtain network-based spillover indicators. We find that linkages in the network are stronger in the bearish case when the risk of spillover is higher. FinTech institutions' risk spillover to financial institutions positively correlates with financial institutions' increase in systemic risk. These results have important policy implications, as they underscore the importance of enhancing the supervision and regulation of FinTech companies, to maintain financial stability.