React Native - How to prevent full screen video mode in IOS?

Simply remove webkit prefix from webkit-playsinline because webkit prefix is no longer required nor it is supported.

Following is the correct and modified code snippet of your code you shared in the question:

import React, { Component } from 'react';
import { WebView, View } from 'react-native';

export default class MyVideoApp extends React.Component{
    render(){
        return(
            <View style={{
                flex: 1,
                flexDirection: 'column',
                justifyContent: 'center',
                alignItems: 'center'
            }}>
                <WebView
                source={{
                    html: '<video playsinline controls autoplay src="https://www.w3schools.com/html/mov_bbb.mp4" ></video>'
                }}
        useWebKit={true}
                originWhitelist={['*']}
                allowsInlineMediaPlayback={true}
                style={{
                    height: 600,
                    width: 400,
                }}/>
            </View>
        );
    }
}