How to put conditional Required Attribute into class property to work with WEB API?

You can implement your own ValidationAttribute. Perhaps something like this:

public class RequireWhenCategoryAttribute : ValidationAttribute
{
    protected override ValidationResult IsValid(object value, ValidationContext validationContext)
    {
        var employee = (EmployeeModel) validationContext.ObjectInstance;
        if (employee.CategoryId == 1)
            return ValidationResult.Success;

        var emailStr = value as string;
        return string.IsNullOrWhiteSpace(emailStr)
            ? new ValidationResult("Value is required.")
            : ValidationResult.Success;
    }
}

public sealed class EmployeeModel
{
    [Required]
    public int CategoryId { get; set; }
    [RequireWhenCategory]
    public string Email { get; set; } // If CategoryId == 1 then it is required
}

This is just a sample. It may have casting issues, and I'm not sure this is the best approach to solve this problem.

Here's my 2 cents. It will give you a nice message like "AssigneeId is required for the current AssigneeType value Salesman" It works for enums too.

[AttributeUsage(AttributeTargets.Property | AttributeTargets.Field, AllowMultiple = false)]
public class RequiredForAnyAttribute : ValidationAttribute
{
    /// <summary>
    /// Values of the <see cref="PropertyName"/> that will trigger the validation
    /// </summary>
    public string[] Values { get; set; }

    /// <summary>
    /// Independent property name
    /// </summary>
    public string PropertyName { get; set; }

    protected override ValidationResult IsValid(object value, ValidationContext validationContext)
    {
        var model = validationContext.ObjectInstance;
        if (model == null || Values == null)
        {
            return ValidationResult.Success;
        }

        var currentValue = model.GetType().GetProperty(PropertyName)?.GetValue(model, null)?.ToString();
        if (Values.Contains(currentValue) && value == null)
        {
            var propertyInfo = validationContext.ObjectType.GetProperty(validationContext.MemberName);
            return new ValidationResult($"{propertyInfo.Name} is required for the current {PropertyName} value {currentValue}");
        }
        return ValidationResult.Success;
    }
}

Use it like this

public class SaveModel {
    [Required]
    public AssigneeType? AssigneeType { get; set; }

    [RequiredForAny(Values = new[] { nameof(AssigneeType.Salesman) }, PropertyName = nameof(AssigneeType))]
    public Guid? AssigneeId { get; set; }
}