import pandas as pd
def sort_and_merge_series(data):
    # Convert list to pandas Series if it's not already a Series
    if isinstance(data, list):
        series = pd.Series(data)
    else:
        series = data
    
    # Sort the series in ascending order
    sorted_series = series.sort_values()
    
    # Extract indices for odd and even positions
    odd_indices = sorted_series.iloc[::2].index
    even_indices = sorted_series.iloc[1::2].index[::-1]  # Reverse the even indices for descending merge
    
    # Concatenate the two parts while preserving indices
    merged_series = pd.concat([sorted_series.loc[odd_indices], sorted_series.loc[even_indices]])
    
    return merged_series