That will depend on the active ingredient in the facial serum.
Some, such as retinol, which boosts both skin cell turnover and collagen production, are certainly more useful to the skin at night, when it's undergoing repair and renewal. Sunlight can also reduce the potency of retinol if applied in the morning.
Other serums, especially anti-ageing serums containing antioxidants like vitamin C, resveratrol, or ferulic acid, are better applied in the morning so they can protect the skin from oxidative stress generated by the sun's rays and other external aggressors during the day.
And in some cases it might depend on what other active ingredients you are using in your routine. For example, salicylic acid and niacinamide are at their most effective at quite different pH (acidity) levels. Salicylic acid serum is formulated with an acidic pH between 3 and 4, but niacinamide works best at a more neutral pH of around 6. Using both at the same time of day compromises their penetration ability and performance, so it makes sense to split them between your morning and evening routines (in this example we'd recommend niacinamide in the morning and salicylic acid at night).