Try the following

awk 'NR%4==2 {gsub(" ", "");} {print;}' input.fastq > output.fastq

Replace the names of the files as appropriate.

ChatGPT also suggests this python script

def remove_spaces_from_fastq(input_file, output_file):
    with open(input_file, 'r') as infile, open(output_file, 'w') as outfile:
        for line_number, line in enumerate(infile, start=1):
            # Modify the second line (sequence line) by removing spaces
            if line_number % 4 == 2:
                line = line.replace(" ", "")

            # Write the modified or unmodified line to the output file
            outfile.write(line)

if __name__ == "__main__":
    input_fastq = "input.fastq"  # Replace with your input FASTQ file
    output_fastq = "output.fastq"  # Replace with the desired output file name

    remove_spaces_from_fastq(input_fastq, output_fastq)

Save as remove_spaces.py and run.

python remove_spaces.py

NOTE: Pay attention to point @Ram has made a couple of times. If the data is corrupt you are best off procuring a new copy.

Did you figure out why those white spaces were introduced? Your data is possibly corrupt and you're working to silence the evidence instead of preserving it.