<p>This paper addresses <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> state estimation for Markovian jumping delayed systems under exogenous disturbances and time-varying delays. To capture the complexity of real-world mode transitions, Markovian jumping delayed systems with interval-valued transition probabilities are considered, further generalized to allow transition probability elements that are exact, interval-bounded, or fully uncertain. A maximum error first and try once discard scheduling protocol, coupled with a dynamic event triggering mechanism, is employed to mitigate data collisions and reduce communication load. Leveraging the binary delta operator, a mode-dependent estimator is designed to asymptotically reconstruct the true system states. By constructing an energy functional and applying stochastic analysis, the estimation error system is shown to achieve mean square asymptotic stability with guaranteed <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(H_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> performance. Estimator gains are obtained via the solution of matrix inequalities. The proposed methodology is validated through two numerical simulations and one practical application, demonstrating its effectiveness and robustness.</p>