<p>ESG firms are promoted as sustainable investments, but their volatility behaviour during crises remains underexplored in emerging markets. This study examines how Indian ESG and conventional market firms respond to crisis shocks and negative news. We analysed daily data from 2016 to 2025 for the Nifty 100 ESG, Nifty 50, Nifty Mid-cap 100, and Nifty Small-cap 100, which represent ESG firms, large-cap firms, mid-cap firms, and small-cap firms listed in Indian market respectively. We use Wavelet Power Spectrum analysis to examine crisis sensitivity and GARCH family models to capture persistence, asymmetry, nonlinearities, and long memory. The wavelet results show that ESG and large-cap firms experience sharp but short-lived volatility spikes during COVID-19 and the Russia-Ukraine war, indicating resilience and quick recovery. Small-cap firms display prolonged volatility across longer time periods, reflecting structural fragility. Mid-cap firms fall between these extremes. EGARCH and TARCH models demonstrate significant asymmetry across all firms. Negative shocks increase volatility substantially more than positive ones. This effect is strongest in mid-cap and small-cap firms. APARCH confirms asymmetric responses in ESG and pronounced nonlinearity in mid-cap and small-cap firms. FIGARCH reveals significant differences in long memory. Mid-cap and small-cap firms show statistically significant long memory, while ESG firms and large-cap firms do not despite their high persistence. ESG firms show significant sensitivity to reputational shocks during crises, though they absorb these impacts quickly without long memory. Standardized ESG disclosure frameworks would reduce the rating ambiguity that triggers panic-driven trading, while investors should prepare for acute but temporary volatility spikes when managing ESG portfolios during systemic events.</p>