Exemplo de consulta com Accepts diferentes (binario x json)

ExemploAcceptController.cs

[HttpGet("contas/{idConta}/extrato")]
[Produces("application/json", "application/pdf")]
public ActionResult<ExtratoModel> GetExtrato([FromHeader] string accept, [FromQuery] string fromData)
{
    string[] acceptedTypes = accept.Split(',')
        .Select(type => MediaTypeHeaderValue.Parse(type))
        .OrderByDescending(type => type.Parameters.FirstOrDefault(p => p.Name == "q")?.Value)
        .Select(type => type.ToString()).ToArray();

    foreach (string acceptedType in acceptedTypes)
    {
        switch (acceptedType)
        {
            case "application/json":

                return new ExtratoModel()
                {
                    Saldo = 12.33,
                    Lancamentos = new List<ExtratoModel.Lancamento>()
                    {
                        new ExtratoModel.Lancamento()
                        {
                            Data = DateTime.UtcNow.ToString("O"),
                            Descricao = "Pagamento",
                            Valor = 123.45
                        }
                    }
                };

            case "application/pdf":

                var pdf = new MemoryStream(); //Seu método que gera o PDF ...

                return new FileContentResult(pdf.ToArray(), "application/pdf")
                {
                    FileDownloadName = "extrato.pdf"
                };
        }
    }

    //Tratamento de erro ...

    Response.StatusCode = 406;
    return null;
}

ExtratoModel.cs

public class ExtratoModel
{
  public double Saldo { get; set; }
  public List<Lancamento> Lancamentos { get; set; } = new List<Lancamento>();
  public class Lancamento
    {
      public string Data { get; set; }
      public string Descricao { get; set; }
      public double Valor { get; set; }
    }
}