How to access non static property from static function in typescript

It's not possible. You can't get an instance property from a static method because there is only one static object and an unknown number of instance objects.

You can, however, access static members from an instance. This will probably be useful for you:

export class User {
    // 1. create a static property to hold the instances
    private static users: User[] = [];

    constructor(public name: string, public password: string) { 
        // 2. store the instances on the static property
        User.users.push(this);
    }

    static findOne(name: string) {
        // 3. find the instance with the name you're searching for
        let users = this.users.filter(u => u.name === name);
        return users.length > 0 ? users[0] : null;
    }
}