To find the value of \(x\) at which the function \(y = x^2 - 2x - 3\) has a minimum, we need to determine the vertex of the parabolic function. The vertex of a parabola of the form \(y = ax^2 + bx + c\) is given by the formula:

\[x_{\text{vertex}} = -\frac{b}{2a}\]

In your case, the coefficients are \(a = 1\) and \(b = -2\). Plugging these values into the formula:

\[x_{\text{vertex}} = -\frac{-2}{2 \cdot 1} = 1\]

So, the value of \(x\) at which the function \(y = x^2 - 2x - 3\) has a minimum is \(x = 1\).