Dynamic partial reconfiguration (DPR) enabled FPGA-based Cloud architecture acts as a flexible and efficient shared environment to facilitates application support to users' request at low cost. While on one hand we need to handle a variety of tasks, such as periodic or sporadic, deadline or non-deadline, high or low critical tasks from the point of producing correct results, on the other hand we are constrained to use untrusted FPGA-based application IP blocks procured from various third-party vendors, which may contain hardware Trojan horse (HTH) affecting throughput and reliability of the Cloud. We propose Trojan-aware processing of tasks by monitored execution of a task on different untrusted cores, and then one more execution is done upon detection of hardware Trojan effects. For this stringent scheduling environment, the proposed dynamic scheduling algorithm is also properly extended to guarantee successful recovery from Trojan effects for all accepted tasks. Experimental results show that our algorithm improves worst-case-response-time for all tasks including non-deadline tasks and achieves lower task rejection rate for the deadline tasks, through judicious non-uniform partitioning of FPGAs based on supported jobs and subsequent better resource utilization, compared to that for existing Trojan-aware scheduling techniques. © 2020 ACM.