We consider target parameter estimation for automotive Phase-Modulated Continuous-Wave (PMCW) radar equipped with one-bit modulo analog-to-digital converters (ADCs) with known folding-counts (Mod-ADC-K). One-bit Mod-ADC-K can save energy and overcome the dynamic range problems of one-bit or low-bit conventional ADCs. However, each one-bit Mod-ADC-K introduces an additional folding making it necessary to devise new target parameter estimation algorithms. The Iterative Adaptive Approach (IAA) is a robust nonparametric spectral estimation algorithm with high resolution. We introduce an extended IAA algorithm, referred to as Mod-IAA for one-bit Mod-ADC-K based target parameter estimation. We incorporate the folding-count data generated by Mod-ADC-K into the likelihood function. This likelihood function is then used to construct a proper cost function. Cyclic and Majorization-Minimization (MM) approaches are employed to iteratively optimize this cost function, to estimate the target parameters. Moreover, we employ a relaxation-based maximum likelihood (ML) approach to iteratively refine the results obtained from Mod-IAA for enhanced off-grid target parameter estimation. We also derive the Cramér-Rao bound (CRB) for the target parameter estimation using one-bit Mod-ADC-K based PMCW radar. Furthermore, to determine the number of targets, we derive the Bayesian Information Criterion (BIC) for the one-bit Mod-ADC-K based PMCW radar system. Finally, we provide numerical examples to demonstrate the advantages of using onebit Mod-ADC-K for target parameter estimation using PMCW radar.