In this paper, the extended Kalman filtering scheme in a distributed manner is presented for state-saturated nonlinear systems (SSNSs), where the randomly occurring cyberattacks (ROCAs) with uncertain occurring probabilities (UOPs) are taken into account. In particular, a novel cyberattack model is constructed by the consideration of false data-injection attacks (FDIAs) and denial-of-service attacks (DoSAs) simultaneously. The ROCAs are described by a series of Bernoulli distributed stochastic variables, where the so-called UOPs are considered and described by the nominal mathematical expectations and error bounds. The major effort is to develop a novel DEKF strategy for SSNSs with consideration of state delay and ROCAs with UOPs. In what follows, an upper bound with respect to the filtering error covariance is derived and minimized by selecting the suitable filter parameter. Besides, the concrete expression of the filter parameter is formed by solving matrix difference equations (MDEs). Meanwhile, a sufficient condition under certain constraints is proposed to testify the boundedness regarding the given upper bound. Finally, we use the experiments and corresponding comparisons to verify the feasibility of the designed extended Kalman filtering approach in a distributed way.